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If the equatoin ax^(2)-6xy+y^(2)+2bx+2cy...

If the equatoin `ax^(2)-6xy+y^(2)+2bx+2cy+d=0` represents a pair of lines whose slopes are m and `m^(2)`, then value (s) of a is /are

A

`a=-8`

B

`a=8`

C

`a=27`

D

`a=-27`

Text Solution

Verified by Experts

The correct Answer is:
2, 4
`m and m^(2)` are the roots of equation
`((y)/(x))^(2)-6((y)/(x))+a=0`
`:. m+m^(2)=6andm^(3)=a`
or `m^(3)+m^(6)+3m^(3)(m+m)=216`
`a+a^(2)+3a*6=216`
`a^(2)+19a-216=0or a=8,a=-27`
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