First determine the center of the circle. The "x-3" portion of the circle equation tells us that the x coordinate is equal to 3. The "y-3" portion of the circle equation tells us that the y coordinate is equal to 3 as well. Therefore, the center of the circle is at (3,3).

To find the distance between (3,3) and (0,0), it is necessary to use the Pythagorean Theorem . Where "a" and "b" are equal to 3

(to visualize, you may draw the two points on a graph, and create a triangle. The line connecting the two points is the hypotenuse, aka "c." )

Remember that the "shifts" involved with circular functions are sort of like those found in parabolas. When you shift a parabola left or right, you have to think "oppositely". A right shift requires you to subtract from the x-component, and a left one requires you to add. Hence, this circle has no horizontal shift, but does shift 6 upward for the vertical component.

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the center point.

The center point is at (0,6) and the circle has a radius of 5.

The equation given represents a circle.

represents the center, and is the radius.

The center is at:

Set up an equation to solve the radius.

The radius is:

The answer is:

Recall what the standard equation of a circle is:

.

is the center of the circle.

Remember that you have to change the signs!

Thus, since our equation is,

your answer for the center is: .

Remember that the shifts for circles work in an opposite manner from what you might think. They are like the parabola's x-component. Hence, a subtracted variable actually means a shift up or to the right, for the vertical and horizontal components respectively. Since the x-component has a "+5", it is shifted left 5. Since the y-component has a , it is shifted upward 12. Therefore, this circle has a center at .

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the center point.

The center point is at and the circle has a radius of 6.

First, recall what the standard equation of a circle: . Your center is (h,k). Remember to flip the signs to get your center for this equation: .

Remember that for the equation of a circle, the lone number to the right of the equals sign is the radius squared.

The general formula for a circle with center at and a radius of is:

Comparing this to the given equation, we can determine the radius.

The center point is at and the circle has a radius of 9.

Remember that the "shifts" involved with circular functions are sort of like those found in parabolas. When you shift a parabola left or right, you have to think "oppositely". A right shift requires you to subtract from the x-component, and a left one requires you to add. Hence, this circle has a positive 3 horizontal shift, and a negative 2 vertical shift.

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the radius and center point.

The center point is at and the circle has a radius of 7.

The question asks us for the sum of these components:

Write the standard form for the equation of a circle.

The value of is and the value of is . The center of the circle is:

To find the radius, set and solve for .

Take the square root of both sides. We only consider the positive value since distance cannot be negative.

The answer is:

Remember that the "shifts" involved with circular functions are sort of like those found in parabolas. When you shift a parabola left or right, you have to think "oppositely". A right shift requires you to subtract from the x-component, and a left one requires you to add. Hence, this circle has a negative 5 horizontal shift, and a negative 22 vertical shift.

You can also remember the general formula for a circle with center at and a radius of .

Comparing this to the given equation, we can determine the radius and center point.

The center point is at and the circle has a radius of 11.

The question asks us for the sum of these components: