Find the equation of the tangent to the curve `sqrt(x)+sqrt(y)=a` , at the point `(a^2//4,\ a^2//4)` .

Answer

`x+y=frac{a^{2}}{2}`

Explanation

Given Eqn. `\sqrt{x}+\sqrt{y}=a`

Differentiate with respect to `x`

`\frac{1}{2 \sqrt{x}}+\frac{1}{2 \sqrt{y}}(\frac{d y}{d x})=0`


`\frac{d y}{d x}=-\frac{\sqrt{x}}{\sqrt{y}}`


At`(\frac{a^{2}}{4}, \frac{a^{2}}{4})` slope `m`, is `-1`


Also as we know equation of the tangent is given by

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


`y-\frac{a^{2}}{4}=-1(x-\frac{a^{2}}{4})`


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