The equation r cos θ=2 a sin^2 θ represents the curve

Correct answer: (C) x^3=y^2(2 a-x). Hint: r cos θ=2 a^2 sin^2 θ ⇒ x (x^2+y^2 )=2 ay^2 ⇒ x^3=y^2(2 a-x)

Q86 / 155 · WBJEE 2024 · Mathematics

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
$x^2=y^2(2 a+x)$
Correct answer
C
$x^3=y^2(2 a-x)$
D
$x^3=y^2(a+x)$

Solution

$\begin{aligned} & \text { Hint: } \quad \mathrm{r} \cos \theta=2 \mathrm{a}^2 \sin ^2 \theta \\ & \Rightarrow \quad \mathrm{x}\left(\mathrm{x}^2+\mathrm{y}^2\right)=2 \mathrm{ay}^2 \\ & \Rightarrow \quad \mathrm{x}^3=\mathrm{y}^2(2 \mathrm{a}-\mathrm{x})\end{aligned}$

Hence, the correct answer is option: 'C'.

The equation $r \cos \theta=2 a \sin ^2 \theta$ represents the curve

Solution

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