Question

The abscissa of the point on the curve $\sqrt{xy}=a+x$ the tangent at which cuts off equal intercepts from the co-ordinate axes is (a > 0)

• A. $\frac{a}{\sqrt{2}}$
• B. $-\frac{a}{\sqrt{2}}$
• C. $a\sqrt{2}$
• D. $-a\sqrt{2}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{a}{\sqrt{2}}$
B $-\frac{a}{\sqrt{2}}$

$y=\frac{{(a+x)}^2}{x}\Rightarrow y=\frac{a^2}{x}+2a+x$

$\frac{dy}{dx}=\frac{-a^2}{x^2}+1=-1$ ( for equal intercepts)

$x^2=\frac{a^2}{2}\Rightarrow x=\pm \frac{a}{\sqrt{2}}$