If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3 x^2-2 x y-15 y^2=0$,…
If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3 x^2-2 x y-15 y^2=0$, then $s: p$ is equal to
4 : 3
2 : 3
3 : 5
3 : 4
Solution
Given pair of lines is
$3 x^2-2 x y-15 y^2=0$
on compare with,
$\begin{aligned}
& a x^2+2 h x y+b y^2=0 \\
\Rightarrow \quad & a=3, h=-1, b=-15
\end{aligned}$
Now, sum of slopes,
$s=m_1+m_2=\frac{-2 h}{b}=\frac{-2(-1)}{-15}=\frac{-2}{15}$
and product of slopes
$p=m_1 m_2=\frac{a}{b}=\frac{3}{-15}=\frac{-3}{15}$
Then, $\quad s: p=\frac{-2}{15}: \frac{-3}{15}=2: 3$