Find the equations of the tangent and the normal to the curve `y^2=4a x` at `(x_1,\ y_1)` at 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}`

At `(x_{1}, y_{1})`

Slope of tangent =`(\frac{d y}{d x})_{(x_{1}, y_{1})}=\frac{2 a}{y_{1}}=m`

Equation of tangent is,

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

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