If the angle between the two lines represented by `2x^(2)+5xy+3y^(2)+6x+7y+4=0` is `tan^(-1)(m)`, then m is equal to

Options

A. `(1)/(5)`
B. `1`
C. `(7)/(5)`
D. `7`

Answer

A

Explanation

Let `theta` be the angle represented by the equation `2x^2+5xy+3y^2+6x+7y+4=0` ...(i)
`therefore theta=tan^(-1)mrArr tan theta=m`
Now, `tan theta=(2sqrt(h^2-ab))/(|a+b|)`
`rArr tan theta=|(2sqrt((25)/(4)-6))/(5)|rArr tan theta =|(1)/(5)|`
`therefore m=(1)/(5)`