If x + y = k is normal to y2 = 12x, then k=? (1) 3 (2) 6 (3) 9 (4) None of these

 Answer: (3) 9

The normal to a parabola is perpendicular to the tangent of the parabola. Also, it will pass through the point of intersection of the tangent to the parabola.

Equation of Normal in Slope Form

The equation of normal to the parabola y2 = 4ax of slope m is given by the equation

y = mx – 2am – am3. Here the point of contact is (am2, -2am)

A normal to the parabola y= 4ax has the equation y = mx – 2am – am3.

Comparing this equation with the given equation x + y = k, we get m = -1
We know that a = 3
So, the equation becomes
y + x = 6 + 3 =9
∴ k = 9


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