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If the curves y^2=6x, 9x^2+by^2=16 inter...

If the curves `y^2=6x`, `9x^2+by^2=16` intersect each other at right angles then the value of b is: (1) 6 (2) `7/2` (3) `4` (4) `9/2`

A

`6`

B

`(7)/(2)`

C

`4`

D

`(9)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `y^(2) = 6x `
`rArr " " 2y (dy)/(dx) = 6 rArr (dy)/(dx) = (3)/(y)`
Slope of tangent at `(x_1, y_1)` is `m_1 = (3)/(y_1)`
Also, ` 9x^(2) + by^(2) = 16`
`rArr " " 18 x + 2by (dy)/(dx) = 0 rArr (dy)/(dx) = (-9x)/(by)`
Slope of tangent at `(x_1, y_1)` is `m_2` = `(-9x_1)/(by_1)`
Since, these are intersection at right angle.
`therefore m_1m_2 = -1 rArr = (27x_1)/( by_1^(2)) = 1 `
`rArr " " ( 27 x_1)/( 6bx _1) = 1 " " [ because y_1^(2) = 6x_1]`
`rArr " " b = (9)/(2)`
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