Write Equations of Rotated Conics in Standard Form
-$24 x y - 7 y ^ { 2 } + 36 = 0$
A) $\frac { y ^ { \prime 2 } } { 9 / 4 } - \frac { x ^ { \prime 2 } } { 4 } = 1$
B) $\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 9 / 4 } = 1$
C) $\frac { y ^ { 12 } } { 9 } - \frac { x ^ { 12 } } { 16 } = 1$
D) $\frac { y ^ { \prime 2 } } { 4 } - \frac { x ^ { \prime 2 } } { 9 / 4 } = 1$

Question

Quizplus · Accepted Answer

The given equation $24xy - 7y^2 + 36 = 0$ is a conic section that can be rotated to eliminate the $xy$ term, resulting in a standard form equation of a hyperbola. The correct transformation leads to the equation $\frac{y'^2}{9/4} - \frac{x'^2}{4} = 1$, which represents a hyperbola centered at the origin with its axes rotated relative to the original coordinate system.

Write Equations of Rotated Conics in Standard Form - 24xy−7y2+36=024 x y - 7 y ^ { 2 } + 36 = 024xy−7y2+36=0

Write Equations of Rotated Conics in Standard Form
- $24 x y - 7 y ^ { 2 } + 36 = 0$