Question

The distance between the two lines represented by the equation $9x^2-24xy+16y^2-12x+16y-12=0$ is

• A. $\frac{8}{5}$
• B. $\frac{6}{5}$
• C. $\frac{11}{5}$
• D. None of these

Answer 1

The correct option is A $\frac{8}{5}$

The above given equation
$9x^2-24xy+16y^2-12x+16y-12=0$ can be factorized as
$(3x-4y+2)(3x-4y-6)=0$
Since both the lines are parallel the distance between them will be
$d=\left|\frac{C_2-C_1}{\sqrt{3^2+4^2}}\right|$
$=\left|\frac{2-(-6)}{5}\right|$
$=\frac{8}{5}$