Write the equation in standard form for the circle passing through (9,3) centered at the origin.

Answer 1

The standard equation for a circle is: (x – h)² + (y – k)² = r² where (h,k) is the center and r is the radius. Since the center is (0,0) this simplifies to

x² + y² = r²

We just need to find r². This can be done using the point on the circle, it is the hypotenuse of the triangle. So, you can use the Pythagorean Theorem.

r²=a²+b²

r²=3²+9² = 90

So the final equation is

x² + y² = 90