Question

A circle has the equation 2x^2+12x+2y^2−16y−150=0.

What are the coordinates of the center, and what is the length of the radius?

Answer 1

`2x {}^(2) + 12x + 2y {}^(2) - 16y - 150 = 0 \\ 2(x {}^(2) + 6x) + 2(y {}^(2) - 8y) - 150 = 0 \\ 2(x + 3) {}^(2) - 3 {}^(2) + 2(y - 4) {}^(2) -4 {}^(2) - 150 = 0 \\ 2(x + 3) {}^(2) + 2(y - 4) {}^(2) - 9 - 16 - 150 = 0 \\ 2((x + 3) { }^(2) + (y - 4) {}^(2) ) = 175 \\ (x + 3) {}^(2) + (y - 4) {}^(2) = ( (175)/(2) ) {}^(2)`

Therefore the coordinates of the center equals to (-3;4)

Length of the radius=

`(175)/(2) = 87.5`