The joint equation of 2 sltitudes of an equailateral triangle is `x^(2)-3y^(2)-4x+6sqrt(3)y-5=0`. The third altitude has equation

Options

A. `x+2=0`
B. `y = sqrt(3)`
C. `x=2`
D. None of these

Answer

C

Explanation

The joint equation ………….
For joint equation
`x^(2)-3y^(2)-4x+6sqrt(3)y-5=0`
`(x-sqrt(3)y+C_(1))(x+sqrt(3)y)+C_(2)) = 0`
So equations of straight line are
`y = (x)/(sqrt(3))+(1)/(sqrt(3)) & y = -(x)/(sqrt(3))+(5)/(sqrt(3))`
Then altitude will also angle `(pi)/(3)` with each lines so equation is `x - 2 =0`