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KCET2021MathematicsParabola

If the parabola y= x²-6 x+ passes through the point (0,2) and has its tangent at x= 3 2 parallel to X -axis, then

Options

  1. A=2, =-2
  2. B=-2, =2
  3. C=2, =2
  4. D=-2, =-2

Correct answer

C. =2, =2

Step-by-step solution

y= x²-6 x+ ...(i) Equation of parabola passes through aligned &(0,2) 2=0-0+ & =2 aligned Differentiating Eq. (i) W.r.t. x , d y d x =2 x-6 aligned ( d y d x )_ x= 3 2 &=2 3 2 -6 &=3 -6 aligned As, the tangent is parallel to X -axis, aligned & & d y d x &=0 & & 3 -6 &=0 & &=2 aligned

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