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AP EAMCET201823 Apr 2018Morning ShiftMathematicsParabolaActual

If 5 x-2 y+k=0 is a tangent to the parabola y^2=6 x , then their point of contact is

Options

  1. A( 6 5 , 6 5 )
  2. B( 6 5 , 6 25 )
  3. C( 6 25 , 6 5 )
  4. D( 6 25 , 6 25 )

Correct answer

C. ( 6 25 , 6 5 )

Step-by-step solution

Given curve y^2=6 x difference w.r.t ' x ' 2 y d y d x =6 Given equation of tangent is 5 x-2 y+k=0 aligned Slope & = 5 2 3 y & = 5 2 y= 6 5 aligned Substitute value of y in y^2=6 x aligned ( 6 5 )^2 & =6 x 36 25 =6 x x & = 6 25 aligned Hence, point of contact is ( 6 25 , 6 5 )

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