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COMEDK2017MathematicsHyperbola

The line 21 x+5 y=116 is a tangent to the hyperbola 7 x²-5 y²=232 . Its point of contact is

Options

  1. A(-6,-2)
  2. B(6,2)
  3. C(6,-2)
  4. D(-6,2)

Correct answer

C. (6,-2)

Step-by-step solution

The line 21 x+5 y=116 is a tangent to 7 x²-5 y²=232 . If P (x₁, y₁ ) is the point of contact, then S₁=0 . aligned & 7 x₁ x-5 y₁ y=232 It is same as 21 x+5 y=116 & 7 x₁ 21 =- 5 y₁ 5 = 232 116 =2 & x₁=6, y₁=-2 . So, P is (6,-2) . aligned

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