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Maths-

General

Easy

Question

The length of subtangent to the curve $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$ at the point $left parenthesis negative a comma blank a right parenthesis$ is

$3 a$
$2 a$
$a$
$4 a$

The correct answer is: $a$

Equation of the curve is $x to the power of 2 end exponent y to the power of 2 end exponent equals a to the power of 4 end exponent$
On differentiating w.r.t. $x$ , we get

$x to the power of 2 end exponent 2 y fraction numerator d y over denominator d x end fraction plus y to the power of 2 end exponent 2 x equals 0$

$rightwards double arrow blank fraction numerator d y over denominator d x end fraction equals fraction numerator negative y over denominator x end fraction$

$rightwards double arrow blank open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript open parentheses negative a comma a close parentheses end subscript equals negative open parentheses fraction numerator a over denominator negative a end fraction close parentheses equals 1$

Therefore, length of subtangent at the point $left parenthesis negative a comma blank a right parenthesis$

$equals fraction numerator y over denominator open parentheses fraction numerator d y over denominator d x end fraction close parentheses end fraction equals fraction numerator a over denominator 1 end fraction equals a$

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