If the acute angle between the pairs of lines `3x^2-7xy+4y^2=0` and `6x^2-5xy+y^2=0` be `theta_1` and `theta_2` respectively, then
(A) `theta_1=theta_2`
(B) `theta_1=2theta_2`
(C) `2theta_1=theta_2`
(D) None of these

Options

A. `theta_1=theta_2`
B. `theta_1=2theta_2`
C. `2theta_1=theta_2`
D. None of these

Answer

A

Explanation

Given that , `theta_1` be the angle between the lines represented by equation `3x^2-7xy+4y^2=0`
`therefore tan theta_(1)=|(2sqrt((49)/(4)-3xx4))/(3+4)|rArrtantheta_(1)=|(1)/(7)|`...(i)
and `theta_(2)` be the angle between the lines represented by equation `6x^2-5xy+y^2=0`
`therefore tan theta_(2)=|(2sqrt((25)/(4)-6))/(6+1)|rArrtantheta_(2)=|(1)/(7)|`....(ii)
From Eqs. (i) and (ii), we get `tantheta_(1)=tantheta_(2)`
`therefore theta_(1)=theta_(2)` .