### Concept (1)

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula. The equation of a circle is (x - h) ^2 + (y - k)^2 = r^2 where r is equal to the radius, and the coordinates (x,y) are equal to the circle center. The variables h and k represent horizontal or vertical shifts in the circle graph.

### Sample Problems (11)

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Equation for a circle centered at (-1,2) with radius 5.

###### Problem 1
How to find the equation for a circle given the center and radius.

Give the center and radius of the circle defined by

2(x − 4)² + 2(y − 1)² = 72
###### Problem 2
How to find the center and radius of a circle given an equation.

Give the center and radius of the circle defined by

x² + y² + 6y − 2x − 15 = 0
###### Problem 3
How to find the center and radius of a circle by completing the square.

Find the equation of a circle that has a diameter with endpoints at (-3,-1) and (5,5).

###### Problem 4
How to use two endpoints of a diameter to create the equation for a circle.
###### Problem 5
How to find the center and midpoint of a circle from the endpoints of the diameter.
###### Problem 6
How to write the equation of a circle from a given radius and center.
###### Problem 7
How to write the equation for a circle from the endpoints of the diameter.
###### Problem 8
How to write the equation for a circle from a graph.
###### Problem 9
How to write the equation for a circle from the center and one point on the circle.
###### Problem 10
How to write the equation for a line that is tangent to a circle.
###### Problem 11
How to transform a general form circle to standard form by completing the square.