A curve $C$ has equation ${{x}^{2}}y+{{y}^{4}}=5$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms o

Question

A curve $C$ has equation ${{x}^{2}}y+{{y}^{4}}=5$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$. [2] Find the exact distance between the two tangents to $C$ that are parallel to the $x$-axis. [3]

Accepted Answer

(a) $\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{2xy}{x^2+4y^3}$ (b) $2\sqrt[4]{5}$ units

2023 HCI P1 Q3

2023 HCI P1 Q3

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