How to find the equation of a circle - Math
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A circle has a diameter starting at 
and ending at 
. What is the equation of the circle?
A circle has a diameter starting at
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Using the distance formula, the diameter is 10 units long, so the radius is 5. Then, by finding the midpoint of the diameter, you know the center of the cirle. Plugging values into the circle equation yields the final answer.
Using the distance formula, the diameter is 10 units long, so the radius is 5. Then, by finding the midpoint of the diameter, you know the center of the cirle. Plugging values into the circle equation yields the final answer.
What is the equation for a circle centered at 
with a radius of 
?
What is the equation for a circle centered at
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The general equation for a circle centered at the origin is given by 
where 
is the radius of the circle.
To translate the origin to the first quadrant we need to subtract the appropriate amount to bring it back to center.
So the equation becomes 
The general equation for a circle centered at the origin is given by
To translate the origin to the first quadrant we need to subtract the appropriate amount to bring it back to center.
So the equation becomes
What is the equation of a circle with diameter 
, that is tangent to the x-axis at the point 
and the y-axis at the point 
?
What is the equation of a circle with diameter
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The equation for a circle is 
where the center of the circle lies at the point 
and the radius of the circle is 
. If we are looking for a circle with a diameter of 
, then its radius must be 
. For the circle to be tangent to the x-axis at the point 
and the y-axis at 
, it must be centered at the point 
. Therefore, the equation of the circle will be 
.
The equation for a circle is
A circle has its center at the point 
and a radius of 
units.
What is the equation of the circle?
A circle has its center at the point
What is the equation of the circle?
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The equation for a circle is
where (h, k) is the center of the circle and r is the radius.
Plugging in the values of 
, 
, and 
, we get
The equation for a circle is
where (h, k) is the center of the circle and r is the radius.
Plugging in the values of
Find the equation of a circle if the radius of the circle is 
and the center is located at the origin.
Find the equation of a circle if the radius of the circle is
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The formula for the equation of a circle is:
The values of 
represent the center, and both values are zero at the origin.
Plug in the known values and reduce.
The formula for the equation of a circle is:
The values of
Plug in the known values and reduce.
Write the equation for a circle with the domain of 
and a range of 
.
Write the equation for a circle with the domain of
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The domain of a circle gives the width of the circle, the range of a circle gives the height of a circle - both of which equal the diameter.
The domain and range numbers are both 6 apart, meaning that the diameter of the circle is 6, which means the radius of the circle is 3.
The halfway point between the domain gives the x-coordinate for the center of the circle, which in this case is 5. 5 is halfway between 2 and 8.
The halfway point between the range gives the y-coordinate for the center of the circle, which in this case is 2. 2 is halfway between -1 and 5.
Now we have all of the information needed to plug into the equation for a circle in standard form as shown below where r is the radius and the center is (h,k):
Given a circle with radius of 3, and center of (5,2) we get the below equation of a circle.
The domain of a circle gives the width of the circle, the range of a circle gives the height of a circle - both of which equal the diameter.
The domain and range numbers are both 6 apart, meaning that the diameter of the circle is 6, which means the radius of the circle is 3.
The halfway point between the domain gives the x-coordinate for the center of the circle, which in this case is 5. 5 is halfway between 2 and 8.
The halfway point between the range gives the y-coordinate for the center of the circle, which in this case is 2. 2 is halfway between -1 and 5.
Now we have all of the information needed to plug into the equation for a circle in standard form as shown below where r is the radius and the center is (h,k):
Given a circle with radius of 3, and center of (5,2) we get the below equation of a circle.
If the point (2,4) is on a circle whose center is at (6,8), which of the following is the standard form of the equation of this circle?
If the point (2,4) is on a circle whose center is at (6,8), which of the following is the standard form of the equation of this circle?
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The standard equation of a circle is 
where 
is the center and r is the radius. Since we were given a point on the circumference of the circle and its center, we use the distance formula to find the radius and then plug the radius and our center point into our equation.
Now substitute the center points and radius into the standard equation of a circle:
The standard equation of a circle is
Now substitute the center points and radius into the standard equation of a circle:
Write the equation for a circle with center 
passing through the point 
Write the equation for a circle with center
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To determine the equation for a circle, we need to know the center and the radius. In this case, we know the center and one of the points on the circle. The radius of the circle is the distance from the center to this point, so to determine it, use the distance formula:
The equation for a circle is written as 
where the center is 
and the radius is r. For this circle, plug in 
and 
:
or more simply
To determine the equation for a circle, we need to know the center and the radius. In this case, we know the center and one of the points on the circle. The radius of the circle is the distance from the center to this point, so to determine it, use the distance formula:
The equation for a circle is written as
Write the equation for a circle passing through the point 
and centered at the origin.
Write the equation for a circle passing through the point
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To determine the equation of the circle, we need to know the radius, or the distance from the origin to the point on the circle. Use the distance formula:
Since the circle is centered at the origin, its equation is 
or more simply 
To determine the equation of the circle, we need to know the radius, or the distance from the origin to the point on the circle. Use the distance formula:
Since the circle is centered at the origin, its equation is
Which of these points is inside the circle
?
Which of these points is inside the circle
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Plugging in the point 
shows that this point is inside the circle, since the left side of the equation will be less than the right:
Plugging in the point
Write the equation for the circle with center 
and radius 
Write the equation for the circle with center
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The equation for a circle is in the form 
where 
is the center and r is the radius.
In this case:
The equation for a circle is in the form
In this case:
What is the equation for a circle centered at 
passing through the point 
What is the equation for a circle centered at
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The equation of a circle is defined by 
where the center is 
and the radius is r. The radius is the distance from the center to any point on the circle, so we can use the distance formula to calculate it:
The equation is then 
or more simplified, 
The equation of a circle is defined by
The equation is then
Write the equation for a circle with center 
and passing through the point 
Write the equation for a circle with center
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To determine the radius of the circle, use the distance formula:
The equation for the circle is 
or more simply 
To determine the radius of the circle, use the distance formula:
The equation for the circle is
What is the equation of a circle that has its center at 
and a radius of 
?
What is the equation of a circle that has its center at
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Recall the standard form for the equation of a circle:
In this equation, 
represents the center of the circle and 
is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center at 
and a radius of 
?
What is the equation of a circle that has its center at
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Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center at 
and a radius of 
?
What is the equation of a circle that has its center at
Tap to see back →
Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center at 
and a radius length of 
?
What is the equation of a circle that has its center at
Tap to see back →
Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center at 
and a radius of 
?
What is the equation of a circle that has its center at
Tap to see back →
Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center of 
and a radius of 
?
What is the equation of a circle that has its center of
Tap to see back →
Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
What is the equation of a circle that has its center of 
and a radius of 
?
What is the equation of a circle that has its center of
Tap to see back →
Recall the standard form for the equation of a circle:
In this equation, represents the center of the circle and is the radius of the circle.
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is:
Recall the standard form for the equation of a circle:
In this equation,
Since the center and radius of the circle are given to us, just substitute in the information itno the standard form of the equation of the circle.
The equation of the given circle is: