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The equation of a normal to the parabola y = x 2 - 6 x + 6 which is perpendicular to the line joining the origin to the vertex of the parabola is

Options

  1. A4 x - 4 y - 11 = 0
  2. B4 x - 4 y + 1 = 0
  3. C4 x - 4 y - 21 = 0
  4. D4 x - 4 y + 21 = 0

Correct answer

C. 4 x - 4 y - 21 = 0

Step-by-step solution

4 x - 4 y - 21 = 0 Here y = x - 3 2 - 3 ⇒ y + 3 = x - 3 2 Hence, the vertex is 3 , - 3 Slope of the line joining origin 0,0 and vertex 3 , - 3 is – 1 Hence, the slope of the normal is 1 Equation of the normal is x - 3 = 1 y + 3 - 2 4 1 - 1 4 1 3 ⇒ 4 x - 4 y - 21 = 0

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