WBJEE · Maths · Area Under Curves
The equation \(r \cos \theta=2 a \sin ^2 \theta\) represents the curve
- A \(\mathrm{x}^3=\mathrm{y}^2(2 a+\mathrm{x})\)
- B \(x^2=y^2(2 a+x)\)
- C \(x^3=y^2(2 a-x)\)
- D \(x^3=y^2(a+x)\)
Answer & Solution
Correct Answer
(C) \(x^3=y^2(2 a-x)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint: } \quad \mathrm{r} \cos \theta=2 \mathrm{a}^2 \sin ^2 \theta \\ & \Rightarrow \quad \mathrm{x}\left(\mathrm{x}^2+\mathrm{y}^2\right)=2 \mathrm{ay}^2 \\ & \Rightarrow \quad \mathrm{x}^3=\mathrm{y}^2(2 \mathrm{a}-\mathrm{x})\end{aligned}\)
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