1. In the xy-plane, a circle has its center at the point with coordinates (4,3), and the origin lies on the circle. The point with which of the following coordinates also lies on the circle?

Question

A. (-4,-3)
B. (3,4)
C. (6,8)
D. (7,7)
E. (9,8)

How do you do this?

Answer 1

The distance of (4,3) from (0,0) is 5. So, the circle is

(x-4)^2 + (y-3)^2 = = 25

Now, you know that if the center were at (0,0), (±3,±4) and (±4,±3) would lie on the circle.

So, shift those possibilities right and up, and see what drops out.

(7-4)^2 + (7,3)^2 = 3^2+4^2 = 25

Answer 2

Wait, why did you use Pythagoreon theorom for a circle above in your explanation? I don't understand why you do that.