Use Rotation of Axes Formulas
-$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0 ; \theta = 45 ^ { \circ }$
A) $\frac { x ^ { \prime 2 } } { 4 } + y ^ { \prime 2 } = 1$
B) $\frac { x ^ { \prime 2 } } { 4 } + \frac { y ^ { \prime 2 } } { 4 } = 1$
C) $\frac { x ^ { \prime 2 } } { 4 } + 2 y ^ { \prime 2 } = 1$
D) $x ^ { \prime 2 } + 4 y ^ { \prime 2 } = 1$

Question

Quizplus · Accepted Answer

The given equation is a conic section. By rotating the axes by $45^\circ$, the equation simplifies to $\frac{x'^{2}}{4} + y'^{2} = 1$, which is an ellipse.

Use Rotation of Axes Formulas - 5x2−6xy+5y2−8=0;θ=45∘5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0 ; \theta = 45 ^ { \circ }5x2−6xy+5y2−8=0;θ=45∘

Use Rotation of Axes Formulas
- $5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0 ; \theta = 45 ^ { \circ }$