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JEE Main20202 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

Let P h , k be a point on the curve y = x 2 + 7 x + 2 , nearest to the line, y = 3 x - 3 . Then the equation of the normal to the curve at P is

Options

  1. Ax + 3 y + 26 = 0
  2. Bx + 3 y - 62 = 0
  3. Cx - 3 y - 11 = 0
  4. Dx - 3 y + 22 = 0

Correct answer

A. x + 3 y + 26 = 0

Step-by-step solution

Tangent at P h , k will be parallel to given line d y d x h , k =   2 h + 7   =   3   ⇒   h = – 2 Point P lies on curve k = ( - 2 ) 2 - 7 × 2 + 2 = - 8 For normal at P ( - 2 , - 8 ) Slope of normal = - 1 3 (Negative inverse of slope of tangent) Equation of normal : x + 3 y + 26 = 0

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