The angle between the pair of lines whose equation is `4x^(2)+10xy+my^(2)+5x+10y=0`is

Options

A. `tan^(-1).(3)/(8)`
B. `tan^(-1).(3)/(4)`
C. `tan^(-1).((2sqrt(25-4m))/(m+4)),m in R`
D. none of these

Answer

B

Explanation

The equation `4x^(2)+10xy+my^(2)+5x+10y=0`
will represent a pair of straight lines, if
`4xxmxx0+2xx5xx(5)/(2)xx5-4xx5^(2)-mxx(25)/(4)-0xx5^(2)=0`
`rArr" "125-100-(25m)/(4)=0rArrm=4`
Let `theta` be the angle between the liner. Then,
`tan theta=(2sqrt(25-4m))/(4+m)=(2sqrt(25-16))/(8)=(3)/(4)rArr theta=tan^(-1)((3)/(4))`