A) \[\frac{a}{2}\]
B) \[2a\]
C) \[a\]
D) \[\frac{a}{3}\]
Correct Answer: C
Solution :
Given,/curve \[{{x}^{2}}{{y}^{2}}={{a}^{4}}\] \[\Rightarrow \] \[{{y}^{2}}=\frac{{{a}^{4}}}{{{x}^{2}}}\] On differentiating, we get \[2y\frac{dy}{dx}=\frac{-2{{a}^{4}}}{{{x}^{3}}}\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{-{{a}^{4}}}{{{x}^{3}}y}\] at \[(-a,a),\frac{dy}{dx}=\frac{-{{a}^{4}}}{-{{a}^{3}}.a}=1\] Now, length of sub tangent to the given curve at \[(-a,a)\] is \[\frac{y}{dy/dx}=\frac{a}{1}=a\]You need to login to perform this action.
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