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 $3x^2+10xy+3y^2=0$ 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 $\frac{y}{x}=-\frac{1}{3}$