If the equation `12x^(2)+7xy-py^(2)-18x+qy+6=0` represents a pair of perpendicular straight lines, then

Options

A. `p=12,q=-1`
B. `p=-12,q=1`
C. `p=12,q=1`
D. `p=1,q=12`

Answer

C

Explanation

The given equation will represent a pair of perpendicular straight lines , if `|{:(12,7//2,-9),(7//2,-p,q//2),(-9,q//2,6):}|=0 and 12-p=0`
`rArr p=12 and |{:(12,7//2,-9),(7//2,-12,q//2),(-9,q//2,6):}|=0`
`P=12 and 12(-72-(q^2)/(4))(-7)/(2)((42)/(2)+(9q)/(2))=9((7q)/(4)-108)=0`
`rArr p=12 and -3q^2-(63)/(2)q+(69)/(2)=0`
`therefore p=12 and q=1`