The angle through which the coordinates axes be rotated so that xy-term in the equation `5x^(2)+4sqrt(3)xy+9y^(2)=0` may beb missing, is

Options

A. `pi//6`
B. `pi//4`
C. `pi//3`
D. `2pi//3`

Answer

C

Explanation

In order to remove xy-term from the equation `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0`, the axes are rotated through an angle `theta` given by
`tan 20 =(2h)/(a-b)`
Here, `a=5,b=9 and h=2 sqrt(3)`
`:. tan 2 theta=(2h)/(a-b)`
`rArr tan theta=(4sqrt(3))/(5-9)=-sqrt(3)rArr2 theta=(2pi)/(3)rArr theta=(pi)/(3)`