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Question: The sum of intercepts of any tangent to \(\sqrt{x} + \sqrt{y} = \sqrt{a}\) with the axes is...

The sum of intercepts of any tangent to x+y=a\sqrt{x} + \sqrt{y} = \sqrt{a} with the axes is

A

a

B

2a

C

a\sqrt{a}

D

2a2\sqrt{a}

Answer

a

Explanation

Solution

Any tangent xx11/2+yy11/2=a\frac{x}{{x_{1}}^{1/2}} + \frac{y}{{y_{1}}^{1/2}} = \sqrt{a}

Ž Sum = a(x11/2+y11/2)=aa=a\sqrt{a}({x_{1}}^{1/2} + {y_{1}}^{1/2}) = \sqrt{a}\sqrt{a} = a