Question

Suppose x is any positive number. Circle 1 has a center at (−2, 7) and a radius of 8x. Circle 2 has a center at (−3, 0) and a radius of 5x. Why is circle 1 similar to circle 2?

Answer 1

(x-center)^2+(y-center)^2=r^2
C1: (x-(-2))^2+(y-7)^2=(8x)^2
C1: (x+2)^2+(y-7)^2=64x^2
C2:(x-(-3))^2+(y-0)^2=(5x)^2
C2: (x+3)^2+y^2=25x^2
C1 is similar to C2 in that they both are centered left of the y-axis, and both have a radius including an x^2 value which is not usual.