A curve has parametric equations $x=\tan \theta $, $y=2\sec \theta $ for \(0\le \theta

Question

A curve has parametric equations $x=\tan \theta $, $y=2\sec \theta $ for $0\le \theta <2\pi $. The equation of the tangent to the curve at the point $P$ with parameter $p$ is given by $y=\left( 2\sin p \right)x+2\cos p$. 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 of $AB$ as $p$ varies.[3] The tangent at $P$ meets the line $y=2x$ at the point $S$ and the line $y=-2x$ at the point $T$. Show that the area of the triangle $OST$ is independent of $p$, where $O$ is the origin.[4]

Accepted Answer

(i) $1 + \frac{1}{4x^2} = \frac{1}{y^2}$ (ii) Area of $\triangle OST = 2$ units$^2$ (independent of $p$)

2018 SRJC P1 Q2

2018 SRJC P1 Q2

Video Solution:

Solution:

Solution locked