If `theta` is the angle between the lines `ax^2 +2hxy + by^2 =0` , then angle between `x^2 + 2xy sectheta + y^2 =0` is

Options

A. `theta `
B. `2 theta `
C. `(theta)/(2)`
D. `3 theta `

Answer

A

Explanation

Angle between the lines ` ax^(2)+2hxy+by^(2)=0`
is ` tan theta=|(2 sqrt(h^(2)-ab))/(a+b)|`
For ` x^(2)+2xy sec theta +y^(2)=0`
`h= sec theta , a=b=1`
`:. tan phi=|(2sqrt(sec^(2) theta-1))/(1+1)|`
`=(2 tan theta )/(2)=tan theta `
`:.` Angle between ` x^(2)+2xy sec theta + y^(2)=0` is theta .