Question

If x + y = k is normal to y² = 12x, then k is ______.

Options

• 3

• 9

• –9

• –3

Answer 1

If x + y = k is normal to y² = 12x, then k is 9.

Explanation:

y² = 12x   .......(i)

Differentiating w.r.t. x, we get

`2y ("d"y)/("d"x)` = 12

⇒ `("d"y)/("d"x) = 6/y`

∴ Slope of the normal = `- 1/(("d"y)/("d"x)) = - y/6`

Slope of the Line x + y = k is –1.

∴ `- y/6` = –1

⇒ y = 6

From (i), x = 3

Putting the values of x and y in x + y = k, we get

k = 9