The value of h for which the equation `3x^2+2hxy-3y^2-40x+30y-75=0` represents a pair of straight lines , are

Options

A. 4,4
B. 4,6
C. 4,-4
D. 0,4

Answer

A

Explanation

We have , `3x^2+2hxy-3y^2-40x+30y-75=0` .....(i)
If Eq.(i) represents pair of straight lines , then `|{:(" "3," "h,-20),(" "h,""-3," "15),(-20," "15,-75):}|=0`
`rArr 3(75xx3-15xx15)-h(-75h+15xx20)-20(15h-60)=0`
`rArr 3(225-225)-h(-75h+300)-20(15h-60)=0`
`rArr 75h^2-300h-300h+1200=0`
`rArr 75h^2-600h+1200=0`
`rArr h^2-8h+16=0`
`rArr h=(8+-sqrt(64-64))/(2)=(8)/(2)=4`
`therefore h=4,4` .