Question

The equation of the bisectors of the angles between the lines represented by the equation $2\left(x + 2\right)^{2}+3\left(x + 2\right)\left(y - 2\right)-2\left(y - 2\right)^{2}=0$ is

• A. $3x^{2}-8xy-3y^{2}-28x+4y+32=0$
• B. $3x^{2}+8xy-3y^{2}+28x-4y+32=0$
• C. $3x^{2}-8xy-3y^{2}+28x-4y+32=0$
• D. $3x^{2}-8xy-3y^{2}+28x-4y-32=0$

Answer 1

Answer: (C)

Equation of the bisectors would be
$\frac{\left(x + 2\right)^{2} - \left(y - 2\right)^{2}}{2 - \left(- 2\right)}=\frac{\left(x + 2\right) \left(\right. y - 2 \left.\right)}{\frac{3}{2}}$
$3\left[x^{2} + 4 x + 4 - y^{2} + 4 y - 4\right]=8 \, \left[x y - 2 x + 2 y - 4\right]$
$3x^{2}+12x-3y^{2}+12y=8xy-16x+16y-32$
$3x^{2}-8xy-3y^{2}+28x-4y+32=0$