Find the equations of the tangent and the normal to the curve `(x^2)/(a^2)-(y^2)/(b^2)=1` at `(sqrt(2)a ,\ b)` at indicated points.

Explanation

`(x^{2} / a^{2})-(y^{2} / b^{2})=1`

or `\quad \frac{2 x}{a^{2}}-\frac{2 y}{b^{2}} \frac{d y}{d x}=0`


or `\quad \frac{d y}{d x}=\frac{b^{2} x}{a^{2} y}`

Slope of tangent at `(\sqrt{2} a, b)=\frac{\sqrt{2} b}{a}`


Slope of normal at `(\sqrt{2} a, b)=-\frac{a}{\sqrt{2} b}`


Equation of tangent is


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