If x + y = k is a normal to the parabola y2 = 12x, then the value of

1.	If x + y = k is a normal to the parabola y2 = 12x, then the value of k is …(a) 3 (b) -1 (c) 1 (d) 9
Answer» (d) 9 Slope of normal = -1 and Slope of tangent = -1 The condition for y = mx + c to be a tangent to the parabola y² = 4ax is c = a/m Here the parabola is y² = 12x ⇒ a = 3 and m = 1 ∴ c = 3/1 = 3 ∴ Equation of tangent is y = x + 3 Solving the parabola and tangent we get the points (3, 6) and (3,-6) ∴ k = -3 or k = 9

If x + y = k is a normal to the parabola y2 = 12x, then the value of k is …(a) 3 (b) -1 (c) 1 (d) 9

Answer»

(d) 9

Slope of normal = -1 and

Slope of tangent = -1

The condition for y = mx + c to be a tangent to the parabola

y² = 4ax is c = a/m

Here the parabola is y² = 12x ⇒ a = 3 and m = 1

∴ c = 3/1 = 3

∴ Equation of tangent is y = x + 3

Solving the parabola and tangent we get the points (3, 6) and (3,-6)

∴ k = -3 or k = 9