Question

Please explain how it’s C?!

Answer 1

The equation of a circle centered at the origin is x² + y² = r², where r is the radius.

Because we know that the circle goes through point (0, -9), we know that the radius of the circle is 9, so the equation of the circle is x² + y² = 9² = x² + y² = 81.

Therefore, to see if the point (8, √17) lies on the circle, we need to substitute these coordinates into the equation:

x² + y² = 81
8² + (√17)² = 81
64 + 17 = 81
81 = 81

So this confirms that the point (8, √17) lies on the circle.

I hope this helps!