Geometry help

Question

Identify the equation of the circle that has its center at (7, -24) and passes through the origin.

Answer 1

The circle with center (h,k) and radius r has equation (x-h)² + (y-k)² = r².

 

Since the center is (7,-24), we have (x-7)² + (y+24)² = r².

 

Since the graph goes through the point (0,0), (-7)² + 24² = r², r² = 625

 

Equation:  (x-7)² + (y+24)² = 625.

 

Answer 2

Draw and label a diagram.

The distance from the center to the origin, (0, 0), is the radius.

This distance is r² = 7² + (-24)²

 

(x - 7)² + y + 24)² = r²