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Two pairs of straight lines have the equ...

Two pairs of straight lines have the equations `y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0`. One line will be common among them if

A

`a+8h-16b=0`

B

`a-8h+16b=0`

C

`a-6h+9b=0`

D

`a+6h+9b=0`

Text Solution

Verified by Experts

The correct Answer is:
2,4
The equation `y^(2)+xy-12x^(2)=0` can be rewritten as
`(y+4x)(y-3x)=0`
or `(y)/(x)=-4,3`
The two pairs will have a line common if -4 or 3 is a root of
`b((y)/(x))^(2)+2h((y)/(x))+a=0`
`:. 9b+6h+a=0or16b-8h+a=0`
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