Question

Prove that the points (0, -5), (4, 3) and (-4, -3) lie on the circle centred at the origin with radius 5.

Answer 1

Distance from center to point on circle must be equal & equal to radius

$A=(0,-5)B(4,3)C(-4,-3)O(0,0)$

$AO=\sqrt{5^2}$ $BO=\sqrt{3^2+4^2}$ $CO=\sqrt{3^2+4^2}$

Hence $CE(0,0)$ is center with radius 5.