A curve $C$ has equation $3{{x}^{2}}-2xy+5{{y}^{2}}=14$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=

Question

A curve $C$ has equation $3{{x}^{2}}-2xy+5{{y}^{2}}=14$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{3x-y}{x-5y}$. [2] Find the exact $x$-coordinates of the points on the curve $C$ at which the tangent is parallel to the $y$-axis. [3] A point $P\left( x,y \right)$ moves along the curve $C$ in such a way that $y$ decreases at a constant rate of $7$ units per second. Given that $x$ increases at the instant when $y=1$, find the corresponding rate of change in $x$. [3]

Accepted Answer

(i) $\frac{dy}{dx}=\frac{3x-y}{x-5y}$; (ii) $x=\pm\sqrt5$; (iii) $\frac{dx}{dt}=3.84$ units/s

2019 DHS P2 Q2

2019 DHS P2 Q2

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