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9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 re...

`9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0` represents two parallel lines. Then

A

`h = 6, f = 2`

B

`h =- 6, f = 2`

C

`h = 6, f =- 2`

D

`h =- 6, f =- 2`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Since the given equation represents a pair of parallel lines, we have `h^(2) = ab rArr h = +-6`
Condition for pair of lines `|{:(9,h,3),(h,4,f),(3,f,-3):}| =0`
`rArr 9f^(2) -6hf +36 = 0`
For `h = 6, f^(2) -4f +4 =0` or `f =2`
For `h =- 6, f^(2)+4f +4 =0` or `f =- 2`
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