Question

If the tangent at any point of the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ meets the co-ordinate axes of A and B then OA+OB=

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

Answer 1

Answer: (A)

2$\sqrt{a}$

Equation of tangent at any point $\sqrt{x}+\sqrt{y}=\sqrt{a}\frac{\sqrt{x}}{\sqrt{a}}+\frac{\sqrt{y}}{\sqrt{a}}=1$
As the $x$ and $y$ intercepts $\left(\sqrt{a}\right)$ in both cases, thus $OA+OB=\sqrt{a}+\sqrt{a}=2\sqrt{a}$