Question : If $x+3y=-3x+y$, then $\frac{x^{2}}{2y^{2}}$ is equal to:
Option 1: $\frac{1}{8}$
Option 2: $\frac{1}{2}$
Option 3: $\frac{1}{4}$
Option 4: $4$
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Correct Answer: $\frac{1}{8}$
Solution :
Given:
$x+3y=-3x+y$
Solution:
⇒ $x+3y+3x-y=0$
⇒ $4x+2y=0$
⇒ $2(2x+y)=0$
⇒ $2x+y=0$
⇒ $y=–2x$
Put the value of $y$ in $\frac{x^{2}}{2y^{2}}$
= $\frac{x^{2}}{2(–2x)^{2}}$
= $\frac{x^{2}}{8x^{2}}$
= $\frac{1}{8}$
Hence, the correct answer is $\frac{1}{8}$.
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