Yefim S. answered • 04/12/21

Math Tutor with Experience

A. y^{2} - 12x + 18y + 153 = 0; y^{2} + 18y + 81 = 12x - 72

(y + 9)^{2} = 12(x - 6)

This is horizontal parabola with vertex at point (6, - 9) and 4p = 12; p = 3. So focus at point (9, - 9).

B. x^{2} + y^{2} - 8x - 6y - 39 = 0; ( x - 4)^{2} + (y - 3)^{2} - 16 - 9 - 39 = 0; (x - 4)^{2} + (y - 3)^{2} = 64.

So, this is circle with center at (4, 3) and radius 8