Write the following in standard form and identify the conic section A. and B. A. y^2-12x+18y+153=0 AND B. x^2+y^2-8x-6y-39=0

Question

Step by Step Solution, please.

Answer 1

A. y² - 12x + 18y + 153 = 0; y² + 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. x² + y² - 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