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

Question

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

Accepted Answer

(a) $t = \displaystyle\frac{1}{4}$; (b) $5x = 25y^2 + 1$

Worked Example 3

Worked Example 3

Video Solution:

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