If the tangent at the point $P$ with co-ordinates $(h, k)$ on the curve $y^{2}=2 x^{3}$ is perpendicular to the straight line $4 x=3 y$, then

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If the tangent at the point $P$ with co-ordinates $(h, k)$ on the curve $y^{2}=2 x^{3}$ is perpendicular to the straight line $4 x=3 y$, then

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kritika · Answer 1 · 2021-12-26T05:12:54+0000

Ans: (B)
Hint : $2 y \frac{d y}{d x}=6 x^{2} \Rightarrow \frac{d y}{d x}=\frac{3 x^{2}}{y}=-\frac{3}{4} \Rightarrow y=-4 x^{2}$ and $y^{2}=2 x^{3}$
$$
\Rightarrow 16 x^{4}=2 x^{3} \Rightarrow x=\frac{1}{8} \quad(x \neq 0)
$$
$$
y=\frac{-1}{16} \quad(y \neq 0)
$$

If the tangent at the point \(P\) with co-ordinates \((h, k)\) on the curve \(y^{2}=2 x^{3}\) is perpendicular to the straight line \(4 x=3 y\), then

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