Question

Change general form of hyperbola into standard: -x^2 + y^2 -16x + 14y - 251 = 0

Answer 1

(y+7)²/364 - (x+8)²/364 = 1

Explanation:

This is the standard form of a vertical hyperbola (y-k)²/a² - (x-h)²/b² = 1

so, (y²+14y+?) - (x²+16x+?) = 251

(y²+14+49)-49 - (x²+16x+64)-64 = 251

(y+7)² - (x+8)² = 251 + 49 + 64

(y+7)² - (x+8)² = 364

(y+7)²/364 - (x+8)²/364 = 1