A curve $C$ has parametric equations $x = 5t^{2}$, $y = 2t$. Find the value of $t$ at the po

Question

A curve $C$ has parametric equations $x = 5t^{2}$, $y = 2t$. Find the value of $t$ at the point on $C$ where the tangent has gradient $0.8$. The normal at the point $P(5p^{2}, 2p)$ on $C$ meets the $x$-axis at point $Q$. Find the Cartesian equation of the locus of the midpoint of $PQ$ as $p$ varies.

Accepted Answer

(a) $t=\frac14$ (b) $5x=25y^2+1$

Applications of Differentiation - Tangents and Normals to Parametric Curves

Applications of Differentiation - Tangents and Normals to Parametric Curves

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