Geometry - How to find the equation of a circle

What is the equation of a circle that has its center at $(5, \frac{1}{4})$ and a radius length of $\frac{1}{5}$ ?

$(x-5)^2+(y-\frac{1}{4})^2=\frac{1}{25}$

$(x-5)^2+(y-\frac{1}{4})^2=\frac{1}{10}$

$(x-\frac{1}{4})^2+(y+5)^2=\frac{1}{25}$

$(x-5)^2-(y+\frac{1}{4})^2=\frac{1}{5}$

Explanation

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:

$(x-5)^2+(y-\frac{1}{4})^2=\frac{1}{25}$

A circle has its center at the point and a radius of units.

What is the equation of the circle?

Explanation

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

Find the equation of a circle if the radius of the circle is and the center is located at the origin.

$x^2+y^2 = \frac{1}{2}$

$x^2+y^2 = \sqrt2$

Explanation

The formula for the equation of a circle is:

The values of $\left ( h,k\right )$ represent the center, and both values are zero at the origin.

Plug in the known values and reduce.

Write the equation for the circle with center and radius

Explanation

The equation for a circle is in the form where is the center and r is the radius.

In this case:

What is the equation for a circle centered at with a radius of ?

$(x-1)^{2}+ (y-2)^{2} = 9$

$(x+2)^{2}+ (y+1)^{2} = 36$

$(x-2)^{2}+ (y+1)^{2} = 18$

$(x+1)^{2}+ (y-2)^{2} = 9$

$(x-1)^{2}+ (y+2)^{2} = -9$

Explanation

The general equation for a circle centered at the origin is given by $x^{2}+y^{2}=r^{2}$ 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 $(x-1)^{2}+(y-2)^{2}=9$

What is the equation of a circle that has its center of and a radius of ?

$(x-19)^2+(y-28)^2=\sqrt{13}$

$(x-19)^2+(y-28)^2=\frac{13}{2}$

Explanation

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:

A circle has a diameter starting at and ending at . What is the equation of the circle?

$(x-6)^{2}+(y-6)^{2}=25$

$(x-6)^{2}+(y-6)^{2}=100$

$(x-4)^{2}+(y-8)^{2}=25$

$(x-6)^{2}+(y-6)^{2}=5$

$(x+6)^{2}-(y+6)^{2}=25$

Explanation

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.

Which of these points is inside the circle

Explanation

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:

What is the equation of a circle that has its center of and a radius of ?

$(x-124)^2+(y-201)^2=\sqrt{15}$

Explanation

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:

What is the equation of a circle that has its center at and a radius of ?

$(x-29)^2+(y+100)^2=\sqrt{14}$

Explanation

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:

How to find the equation of a circle

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation