Find the asymptotes of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$$
A) $y - 4 = ( x - 3 )$ and $y - 4 = - ( x - 3 )$
B) $y + 3 = ( x + 4 )$ and $y + 3 = - ( x + 4 )$
C) $y - 3 = ( x - 4 )$ and $y - 3 = - ( x - 4 )$
D) $y - 4 = \frac { 1 } { 2 } ( x - 3 )$ and $y - 4 = - \frac { 1 } { 2 } ( x - 3 )$

Question

Quizplus · Accepted Answer

The equation of the hyperbola can be rewritten in the standard form by completing the squares: $(x^2 - 6x) - (y^2 - 8y) = 11$. Completing the squares gives $(x - 3)^2 - (y - 4)^2 = 16$. The asymptotes of a hyperbola in the form $(x - h)^2 - (y - k)^2 = a^2$ are given by $y - k = \pm (x - h)$, leading to the asymptotes $y - 4 = \pm (x - 3)$.

Find the Asymptotes of the Hyperbola x2−y2−6x+8y−11=0x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0x2−y2−6x+8y−11=0

Find the Asymptotes of the Hyperbola $x ^ { 2 } - y ^ { 2 } - 6 x + 8 y - 11 = 0$