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AP EAMCET201923 Apr 2019Morning ShiftMathematicsParabolaActual

For any non-zero real value of (m ), the equation of the parabola to which the line (m x-y+10+m^2=0 ) is a tangent, is

Options

  1. A(x^2=y-10 )
  2. B(y^2=4(x-2) )
  3. C(x^2=-4(y-10) )
  4. D(x^2=-4 y )

Correct answer

C. (x^2=-4(y-10) )

Step-by-step solution

Given, equation of tangent to the parabola is ( aligned m x-y+ (10+m^2 ) & =0 m^2+m x+(10-y) & =0 aligned ) Since, above line is tangent, then (D=0 ) ( aligned b^2-4 a c & =0 x^2-4 1 (10-y) & =0 x^2 & =4(10-y) x^2 & =-4(y-10) aligned ) Hence, answer is (c).

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