Question

Point of the curve y² = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.

Options

• (5, 3)

• `(- 1/2, -3)`

• (5, –3)

• `(3/2, 3)`

Answer 1

Point of the curve y² = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is (5, 3).

Explanation:

y² = 3(x – 2)  .....(i)

Differentiating w.r.t. x, we get

`2y ("d"y)/("d"x)` = 3

⇒ `("d"y)/("d"x) = 3/(2y)`

∴ Slope of the normal= `(-1)/(("d"y)/("d"x)) = (-2y)/3`

Slope of the given line = –2,

Since the normal is parallel to the given line, y = 3.

From (i), x = 5

∴ The required point is (5, 3).