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 the above

Answer

B

Explanation

Condition for pair of lines , `abc+2fgh-af^2-bg^2-ch^2=0`
`therefore 4xxmxx0+2xx5xx(5)/(2)xx5-4(5)^2-m((5)/(2))^2-0(5)^2=0`
`125-100-(25m)/(4)=0rArr m=4`
Now, the angle between lines is. `tantheta=(2sqrt(h^2-ab))/(a+b)=(2sqrt(25-16))/(8)`
`rArr tan theta =(3)/(4)rArr theta=^(-1)(3)/(4)`