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If 4x^(2)+ py^(2) =45 and x^(2)-4y^(2) =...

If `4x^(2)+ py^(2) =45` and `x^(2)-4y^(2) =5` cut orthogonally, then the value of p is

A

`1//9`

B

`1//3`

C

3

D

9

Text Solution

Verified by Experts

The correct Answer is:
D
Slope of `1^(st)` curve `((dy)/(dx))_(I) =- (4x)/(py)`
Slope of `2^(nd)` curve `((dy)/(dx))_(II) = (x)/(4y)`
For orthogonal intersection `(-(4x)/(py)) ((x)/(4y)) =-1`
`rArr x^(2) = py^(2)`
`:.` From 1st curve `5x^(2) = 45`
`:. X = 3`
`:. y =1`
`:. p(1) = (3)^(2) = 9 rArr p = 9`.
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