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Manipal MET2015MathematicsApplication of Derivatives

The two tangents to the curve a x^2+2 h x y+b y^2=1, a 0 at the points, where it crosses X -axis, are

Options

  1. Aparallel
  2. Bperpendicular
  3. Cinclined at an angle 4
  4. DNone of these

Correct answer

A. parallel

Step-by-step solution

At the point where the given curve crosses X -axis, we have y=0 a x^2=1 [putting y=0 in a x^2+2 h y x+b y^2=1 ] x= 1 a Thus, the given curve cuts X -axis at P ( 1 a , 0 ) and Q (- 1 a , 0 ) . Now, a x^2+2 h x y+b y^2=1 On differentiating both sides w.r.t. x , we get 2 a x+2 h (x d y d x +y )+2 b y d y d x =0 array ll & d y d x =- a x+h y h x+b y & [ d y d x ]_P=- a h and [ d y d x ]_Q=- a h & [ d y d x ]_p= [ d y d x ]_Q array Hence, the tangents are parallel.

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