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

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

W

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