Question

The slopes of the lines given by the equation $ 3x^{2} + 10xy + 3y^{2} − 15x − 21y + 18 = 0 $ are

• A. $ 3 $ and $- \frac{1}{3} $
• B. $ -3 $ and $ -\frac{1}{3} $
• C. $ -3 $ and $ \frac{1}{3} $
• D. $ -3 $ and $ \frac{1}{3} $

Answer 1

Answer: (B)

Lines $3 x^{2}+10 x y+3 y^{2}=0$ are passing through origin and parallel to given lines. It can be rewritten as
$3\left(\frac{y}{x}\right)^{2}+10\left(\frac{y}{x}\right)+3=0$
$\Rightarrow 3\left(\frac{y}{x}\right)^{2}+9\left(\frac{y}{x}\right)+\left(\frac{y}{x}\right)+3=0$
$\Rightarrow \frac{y}{x}=-3$
and $\frac{y}{x}=-\frac{1}{3}$