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AP EAMCET2007MathematicsApplication of Derivatives

The lengths of tangent, subtangent, normal and subnormal for the curve y=x^2+x-1 at (1,1) are A, B, C and D respectively, then their increasing order is

Options

  1. AB, D, A, C
  2. BB, A, C, D
  3. CA, B, C, D
  4. DB, A, D, C

Correct answer

D. B, A, D, C

Step-by-step solution

Given circle is y=x^2+x-1 and point aligned & (x₁, y₁ )=(1,1) & d y d x =2 x+1 aligned At (1,1), d y d x =3=m Now, length of tangent A= | y₁ 1+m^2 m |= | 1 1+9 3 |= 10 3 length of subtangent B= | y₁ m |= 1 3 length of normal C= |y₁ 1+m^2 |=|1 1+9 |= 10 and length of subnormal D= |y₁ m |=3 Now, increasing order is B, A, D, C .

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