Additional Concepts
-$24 x y - 7 y ^ { 2 } + 36 = 0 ;$ Find the equations of the asymptotes.
A) $y ^ { \prime } = - \frac { 4 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 4 } { 3 } x ^ { \prime }$
B) $y ^ { \prime } = - \frac { 3 } { 4 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 3 } { 4 } x ^ { \prime }$
C) $y ^ { \prime } = - \frac { 2 } { 3 } x ^ { \prime }$ and $y ^ { \prime } = \frac { 2 } { 3 } x ^ { \prime }$
D) $y ^ { \prime } = - \frac { x ^ { \prime } } { 3 }$ and $y ^ { \prime } = \frac { x ^ { \prime } } { 3 }$

Question

Quizplus · Accepted Answer

The given equation is of a hyperbola. The slopes of the asymptotes for a hyperbola $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$ can be found using the formula $m = \pm \sqrt{\frac{A-C \pm \sqrt{(A-C)^2 + B^2}}{B}}$. For the given equation, $A=0$, $B=24$, and $C=-7$, leading to $m = \pm \frac{4}{3}$, which corresponds to the slopes of the asymptotes.

Additional Concepts - 24xy−7y2+36=0;24 x y - 7 y ^ { 2 } + 36 = 0 ;24xy−7y2+36=0;

Additional Concepts
- $24 x y - 7 y ^ { 2 } + 36 = 0 ;$