Find the equation of the bisectors of the angles between the lines joining the origin to the point of intersection of the straight line `x-y=2` with the curve `5x^2+11 x y+8y^2+8x-4y+12=0`

Answer

`x^(2)+30xy-y^(2)=0`

Explanation

The equation of lines joining the origin to the points of intersection of the given line and curve is
`5x^(2)+11xy-8y^(2)+(8x-4y)((x-y)/(2))+12((x-y)/(2))^(2)=0`
or `12x^(2)-xy-3y^(2)=0`
The equation of bisectors is
`(x^(2)-y^(2))/(12-(-3))=(xy)/(-1//2)`
or ` x^(2)+30xy-y^(2)=0`