A curve has parametric equations $x= an heta $, $y=2\sec heta $ for $0\le heta The equation o

Question

A curve has parametric equations $x=	an 	heta $, $y=2\sec 	heta $ for $0\le 	heta The equation of the tangent to the curve at the point $P$ with parameter $p$ is given by $y=\left( 2\sin p ight)x+2\cos p$. The tangent at $P$ meets the $x$ and $y$ axes at the points $A$ and $B$ respectively. Find the Cartesian equation of the locus of the mid-point $AB$ as $p$ varies.

Accepted Answer

$\displaystyle\frac{1}{4x^2} = \frac{1}{y^2} - 1$

2018 SRJC P2 Q2 (i)

2018 SRJC P2 Q2 (i)

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