If the angle between the lines represented by the equation `y^2+kxy-x^2tan^2A=0 is 2A`, then K is equal to

Options

A. 0
B. 1
C. 2
D. tan A

Answer

A

Explanation

Given , 2A is the angle between the lines represented by equation `y^2+k xy-x^2tan^2A=0` ......(i)
`therefore tan2A=(2sqrt(h^2-ab))/(|a+b|)=(2sqrt((k^2)/(4)+tan^2A))/(|1-tan^2A|)`
`rArr (2tanA)/(1-tan^2A)=(2sqrt((k^2)/(4)+tan^2A))/(|1-tan^2A|)`
`rArr tan^2A=(k^2)/(4)+tan^2A`
`rArr (k^2)/(4)=0rArr k^2=0`
`therefore k=0` .