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AP EAMCET20226 Jul 2022Morning ShiftMathematicsHyperbolaActual

If the line 3 x-m y+5=0 is a tangent to the hyperbola 3 x^2-4 y^2=300 then the square of the Y- intercept made by this tangent line is

Options

  1. A25 3
  2. B35 3
  3. C45 7
  4. D15 7

Correct answer

D. 15 7

Step-by-step solution

3 x^2-4 y^2=300 x^2 100 - y^2 75 =1 and 3 x-m y+5=0 y= 3 m x+ 5 m Now, for condition of tangents: aligned & c ^2= a ^2 ~m ^2- n ^2 25 ~m ^2 =100 9 ~m ^2 -75 & m ^2= 35 3 aligned Square of y - intercept of x -radius c = 25 ~m ^2 =25 3 35 = 15 7

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