Question

If the curves y² = 6x, 9x² + by² = 16 intersect each other at right angles, then the value of b is ______

विकल्प

• `7/2`

• 4

• `9/2`

• 6

Answer 1

If the curves y² = 6x, 9x² + by² = 16 intersect each other at right angles, then the value of b is `underline(9/2)`.

Explanation:

Let the given curves intersect each other at P(x₁, y₁).

y² = 6x

Differentiating w.r.t. x, we get

`2ydy/dx = 6 ⇒ (dy/dx)_p = 3/y_1`

9x² + by² = 16

Differentiating w.r.t. x, we get

`18x + 2bydy/dx = 0`

⇒ `(dy/dx)_p = -(9x_1)/(by_1)`

Since the given curves intersect each other at right angles, `(3/y_1)((-9x_1)/(by_1)) = -1` 

⇒ `(27x_1)/(by_1^2)= 1`

⇒ b = `9/2` .................`[y_1^2 = 6x_1]`