If (2, −7) and (8, 15) are the endpoints of a diameter of a circle, what is the equation of the circle? A) (x + 5)2 + (y − 4)2 = 60 B) (x − 5)2 − (y − 4)2 = 80 C) (x − 5)2 − (y + 4)2 = 110 D) (x − 5)2 + (y − 4)2 = 130

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb