Give the equation of the circle centered at the origin and passing through the point (0, -5)

Question

Writing the equation of a circle centered at the origin given its radius or a point on the circle

Answer 1

The graph of (x-h)² + (y-k)² = r² is the circle with center (h,k) and radius r.  

 

So, if the center is (0,0), the equation is (x-0)² + (y-0)² = r²

 

Since (0, -5) is on the graph, we have 0² + (-5)² = r².  So, r² = 25

 

Equation of circle:  x² + y² = 25.