If the equation given by `hxy+10x+6y+4=0` represents a pair of lines, then h is equal to

Explanation

The given equation is , `kxy+10x+6y+4=0`
On comparing the above equation with the general equation, `ax^(2)+2hxy+by^(2)+2gx+2gx+2fy+c=0,`we get,
`a=0,b=0,2h=k,2g=10,2f=6,c=4h=k//2,g=5,f=3`
`|{:(a,h,g),(h,b,f),(g,f,c):}|=0`
`|{:(0,(k)/(2),5),((k)/(2),0,3),(5,3,4):}|=0`
`0-(k)/(2)(2k-15)+5((3k)/(2)-0)=0`
`-k^(2)+(15k)/(2)+(15k)/(2)=0`
`-k^(2)=(-30k)/(2)` k=15