2019 RVHS P2 Q4
2019 RVHS P2 Q4
7 marks
Prelims
The parametric equations of a curve are
\(x=\sin t\), \(y=\cos t\), where \(0 < t < \frac{\pi }{2}\).
- Sketch the graph of the curve.[1]
- Show that the equation of the tangent to the curve at the point where \(t=p\) is given by the equation \(y=-\left( \tan p \right)x+\sec p\).[3]
- Given that the above tangent meets the \(x\)-axis at the point \(P\) and the \(y\)-axis at the point \(Q\), find the coordinates of the mid-point \(M\) of \(PQ\) in terms of \(p\).Hence, determine the cartesian equation of the locus of \(M\).[3]
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Answer:(iii) The Cartesian equation of the locus of \({M}\) is \({\frac{1}{x^2} + \frac{1}{y^2} = 4}\) or \({x^2 + y^2 = 4x^2 y^2}\).
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