Find the equations of the tangent and the normal to the curve `y^2=4a\ x` at `(a//m^2,\ 2a//m)` at the indicated points

Explanation

`y^{2}=4 a x`

Differentiating both sides w.r.t.x,

`2 y \frac{d y}{d x}=4 a `

`\Rightarrow \frac{d y}{d x}=\frac{2 a}{y}`

Given `(x_{1}, y_{1})=(\frac{a}{m^{2}}, \frac{2 a}{m})`

Slope of tangent =`(\frac{d y}{d x})_{(\frac{a}{m^{2}}, \frac{2 a}{m})}=\frac{2 a}{(\frac{2 a}{m})}=m`

Equation of tangent is,

`y-y_{1}=m(x-x_{1}) `

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