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Maths-

General

Easy

Question

The length of the subtangent to the curve $x to the power of 2 end exponent plus x y plus y to the power of 2 end exponent equals 7$ at $left parenthesis 1 comma blank minus 3 right parenthesis$ is

3
5
$\frac{3}{5}$
15

The correct answer is: 15

Given curve is $x to the power of 2 end exponent plus x y plus y to the power of 2 end exponent equals 7$
$rightwards double arrow blank 2 x plus x fraction numerator d y over denominator d x end fraction plus y plus 2 y fraction numerator d y over denominator d x end fraction equals 0$

$rightwards double arrow blank fraction numerator d y over denominator d x end fraction equals negative fraction numerator left parenthesis 2 x plus y right parenthesis over denominator x plus 2 y end fraction$

$rightwards double arrow blank open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis 1 comma blank minus 3 right parenthesis end subscript equals fraction numerator negative left parenthesis 2 minus 3 right parenthesis over denominator left parenthesis 1 minus 6 right parenthesis end fraction equals negative fraction numerator 1 over denominator 5 end fraction$

$therefore$ Length of subtangent $equals fraction numerator y over denominator fraction numerator d y over denominator d x end fraction end fraction equals fraction numerator negative 3 over denominator fraction numerator 1 over denominator negative 5 end fraction end fraction equals 15$

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