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

Answer:

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

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

Length of the radius=

$\frac{175}{2} = 87.5$