Question

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

Options

• 2

• 4

• `9/2`

• 3

Answer 1

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

Explanation:

y² = 6x, 9x² + by² = 16

Differentiating above two curves w.r.t. x, we get

`2y(dy/dx)` = 6

⇒ `(dy/dx)_1 = m_1 = 3/y`

`d/(dx)(9x^2 + by^2 - 16)` = 0

`18x + 2by xx (dy/dx)_2` = 0

⇒ `(dy/dx)_2 = (-18x)/(2by) = (-9x)/(by)`

m₁ × m₂ = –1

`3/y xx (- (9x)/(by))` = –1

`(27x)/(by^2)` = 1

⇒ 27 = b × 6(y² = 6x)

⇒ b = `27/6 = 9/2`