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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