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.

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:

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:

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 50 horizontal shift, and a negative 29 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 13.

The question asks us for the sum of these components:

The equation for a circle of radius  centered on point  has the equation 

Just as with linear equations, the horizontal and vertical shifts are opposite of their sign, and are inside the parentheses. The equation of a circle simply must be memorized.

So the circle is centered on point , and plug those in and it yields the formula of the circle.

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." )

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:  

Recall that the standard equation of a circle is . Therefore, in this case . Square root both sides to find your radius. can be simplified to , which is your answer.

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: .