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Manipal MET2024MathematicsParabola

If two tangents drawn from the point (h, k) to the parabola y^2=64 x be such that the slope of one tangent is 8 times of the other, then the value of k^2 2 h is

Options

  1. A9
  2. B27
  3. C81
  4. D162

Correct answer

C. 81

Step-by-step solution

Let the equation of tangent is y=m x+ 16 m [ a=16] It passes through (h, k) Then, k=m h+ 16 m m^2 h+16-m k=0 According to the question, roots of the equation will be m₁ and 8 m₁ . So, m₁+8 m₁= k h 9 m₁= k h ...(i) and m₁ 8 m₁= 16 h 8 m₁^2= 16 h ...(ii) By solving these equations, we get k^2 2 h =81

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