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​Q . SHOW THAT THE SUM OF THE INTERCEPTS OF THE TANGENT TO THE CURVE - x 1/2 + y 1/2 = a 1/2 ON THE COORDINATE AXES IS CONSTANT.

​Q . SHOW THAT THE SUM OF THE INTERCEPTS OF THE TANGENT TO THE CURVE -
   x1/2 + y1/2 = a1/2 ON THE COORDINATE AXES IS CONSTANT.

Grade:Select Grade

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

\sqrt{x} + \sqrt{y} = \sqrt{a}
Lets take the parametric coordinates of the curve,
x = \frac{a}{4}cos^{2}\theta
\frac{dx}{d\theta } = \frac{a}{4}2cos\theta (-sin\theta)
y = \frac{a}{4}sin^{2}\theta
\frac{dy}{d\theta } = \frac{a}{4}2sin\theta cos\theta

\Rightarrow \frac{dy}{dx} = -1
Equation of tangent:
(y-\frac{a}{4}sin^{2}\theta ) = -(x-\frac{a}{4}cos^{2}\theta )
x + y = \frac{a}{4}
Hence proved.

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