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MHT CET202615 April 2026Morning ShiftMathematicsHyperbolaActual

If the line 4x + 3y = 7 touches the hyperbola x^2 - y^2 = 7 , then the sum of the co-ordinates of the point of contact is...

Options

  1. A4
  2. B7
  3. C1
  4. D0

Correct answer

C. 1

Step-by-step solution

The equation of the given hyperbola is x^2 - y^2 = 7 . Let the point of contact be (x₁, y₁) . The equation of the tangent to the hyperbola at this point is given by x x₁ - y y₁ = 7 . The given equation of the line is 4x + 3y = 7 . Since both equations represent the same tangent line, we can compare their corresponding coefficients: x₁ = 4 -y₁ = 3 y₁ = -3 The point of contact is (4, -3) . The sum of the coordinates of the point of contact is 4 + (-3) = 1 . Answer: 1

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