If the sum of slopes of lines represented by $a x^2+8 x y+5 y^2=0$ is twice their product, then $\mathrm{a}=$
If the sum of slopes of lines represented by $a x^2+8 x y+5 y^2=0$ is twice their product, then $\mathrm{a}=$
-4
5
-2
-8
Solution
We have $a x^2+8 x y+5 y^2=0$
Here $\mathrm{m}_1+\mathrm{m}_2=\frac{-8}{5}, \mathrm{~m}_1 \mathrm{~m}_2=\frac{\mathrm{a}}{5}$
As per condition given, we write
$\left(-\frac{8}{5}\right)=2\left(\frac{\mathrm{a}}{5}\right) \Rightarrow \mathrm{a}=-4$