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AP EAMCET2014MathematicsCircle

The slopes of the focal chords of the parabola y^2=32 x , which are tangents to the circle x^2+y^2=4 , are

Options

  1. A1 2 , -1 2
  2. B1 3 , -1 3
  3. C1 15 , -1 15
  4. D2 5 , -2 5

Correct answer

C. 1 15 , -1 15

Step-by-step solution

Given equation of circle is x^2+y^2=(2)^2 The equation of tangent to the circle is y=m x 2 1+m^2 ( y=m x r 1+m^2 ) Also, equation of parabola is y^2=32 x Focus of parabola is (8,0) . Since, the line passes through focus (8,0) . aligned & 0=8 m 2 1+m^2 & -4 m= 1+m^2 & 16 m^2=1+m^2 & 15 m^2=1 & m^2= 1 15 & m= 1 15 & aligned

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