Question

The point on the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ , the normal at which is parallel to the $x-$ axis, is:

• A. $(0,0)$
• B. $(0,a)$
• C. $(a,0)$
• D. $(a,a)$

Answer 1

Answer: (B)

The normal is parallel to $x-$ axis, if $\frac{dx}{dy}=0$
Given equation of curve is $\sqrt{x}+\sqrt{y}=\sqrt{a}$ ... (i)
On differentiating w.r.t. $x,$
we get $\frac{1}{2\sqrt{x}}+\frac{1}{2\sqrt{y}}=\frac{dy}{dx}=0$
$\Rightarrow$ $\frac{dx}{dy}=\sqrt{\frac{x}{y}}$
Since, the normal is parallel to $x-$ axis.
$\therefore \frac{dx}{dy}=0$
$\Rightarrow -\sqrt{\frac{x}{y}}=0$
$\Rightarrow x=0$
$\therefore$ From Eq. (i) $y=a$
$\therefore$ Required point is $(0,a)$ .