Use Rotation of Axes Formulas
-$7 x ^ { 2 } + 6 \sqrt { 3 } x y + y ^ { 2 } - 43 = 0 ; \theta = 30 ^ { \circ }$
A) $\frac { x ^ { 2 } } { \frac { 43 } { 10 } } - \frac { y ^ { \prime 2 } } { \frac { 43 } { 2 } } = 1$
B) $\frac { x ^ { \prime 2 } } { \frac { 43 } { 10 } } + \frac { y ^ { \prime 2 } } { \frac { 43 } { 2 } } = 1$
C) $\frac { x ^ { \prime 2 } } { \frac { 1 } { 10 } } - \frac { y ^ { \prime 2 } } { \frac { 1 } { 2 } } = 1$
D) $\frac { x ^ { \prime 2 } } { \frac { 1 } { 10 } } - \frac { y ^ { \prime 2 } } { \frac { 43 } { 2 } } = - 1$

Question

Quizplus · Accepted Answer

The correct answer is A because the given equation is an ellipse and the rotation of axes formulas are used to find the new equation of the ellipse after rotation. The new equation is in the form of $\frac { x ^ { \prime 2 } } { a ^ { 2 } } - \frac { y ^ { \prime 2 } } { b ^ { 2 } } = 1$ where $a^2=\frac{43}{10}$ and $b^2=\frac{43}{2}$.

Use Rotation of Axes Formulas - 7x2+63xy+y2−43=0;θ=30∘7 x ^ { 2 } + 6 \sqrt { 3 } x y + y ^ { 2 } - 43 = 0 ; \theta = 30 ^ { \circ }7x2+63​xy+y2−43=0;θ=30∘

Use Rotation of Axes Formulas
- $7 x ^ { 2 } + 6 \sqrt { 3 } x y + y ^ { 2 } - 43 = 0 ; \theta = 30 ^ { \circ }$