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Question

Mathematics Question on Application of derivatives

The length of the subtangent to the curv x2y2=a4x^2y^2 = a^4 at (a,a)(-a, a) is

A

3a3a

B

2a2 a

C

aa

D

4a4a

Answer

2a2 a

Explanation

Solution

We have, x2y2=a4y2=a4x2x^2y^2 = a^4 \Rightarrow \:\: y^2 = \frac{a^4}{x^2}
Differentiating w.r.t. x, we get
2ydydx=2a4x32y \frac{dy}{dx} = \frac{-2a^{4}}{x^{3}}
[dydx](a,a)=2a42(a)3.a=1\left[\frac{dy}{dx}\right]_{\left(-a,a\right)} = \frac{-2a^{4}}{2\left(-a\right)^{3}.a}=1
Length of subtangent =ydydx=a1=a= \left|\frac{y}{dy dx}\right| =\left|\frac{a}{1}\right|=a