Circles in the Coordinate Plane

Question

Circle has its center at the point (-5,-8) and it passes through the point (2,-8). Complete the equation:

X - [?]squared + (Y - [?]squared = [?]

Answer 1

The standard form of a circle is (x - h)² + (y - k)² = r², where the center is (h, k) and r = radius

The first step is to plug in the center point. Note that if the circle x-value and y-values are negative then the equation changes to a positive value:

(x + 5)² + (y + 8)² = r²

To find the radius you must put the point that the circle passes through into the equation as the x and y:

(2 + 5)² + (-8 + 8)² = r²

Solve for r²:

7² + 0² = r²

7² = r² = 49

Equation of the circle is: (x + 5)² + (y + 8)² = 49