The point $P\left( x,y \right)$ moves along a curve of which equation is given by ${{\left( 2x+y \ri

Question

The point $P\left( x,y \right)$ moves along a curve of which equation is given by ${{\left( 2x+y \right)}^{2}}+3{{\left( x-y \right)}^{2}}=16$. Find the gradient of the curve at $P$, [2] the relationship between $x$ and $y$ if the normal at $P$ is parallel to the $x$-axis, [2] the equation of the normal at $P$ where the curve cuts the negative $y$-axis. [3]

Accepted Answer

(i) $\dfrac{y-7x}{4y-x}$; (ii) $x = 4y$; (iii) $y = -4x - 2$

2013 RVHS P1 Q5

2013 RVHS P1 Q5

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