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