Question:
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
Updated On: May 11, 2024
- $3a $
- $2 a $
- $a $
- $4a $
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The Correct Option is B
Solution and Explanation
We have, $x^2y^2 = a^4 \Rightarrow \:\: y^2 = \frac{a^4}{x^2}$
Differentiating w.r.t. x, we get
$2y \frac{dy}{dx} = \frac{-2a^{4}}{x^{3}}$
$ \left[\frac{dy}{dx}\right]_{\left(-a,a\right)} = \frac{-2a^{4}}{2\left(-a\right)^{3}.a}=1 $
Length of subtangent $= \left|\frac{y}{dy dx}\right| =\left|\frac{a}{1}\right|=a $
Differentiating w.r.t. x, we get
$2y \frac{dy}{dx} = \frac{-2a^{4}}{x^{3}}$
$ \left[\frac{dy}{dx}\right]_{\left(-a,a\right)} = \frac{-2a^{4}}{2\left(-a\right)^{3}.a}=1 $
Length of subtangent $= \left|\frac{y}{dy dx}\right| =\left|\frac{a}{1}\right|=a $
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Application of Derivatives
Various Applications of Derivatives-
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