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

  1. 3 a  
  2. 2 a  
  3. a  
  4. 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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