If the equation $8 x^2+8 x y+2 y^2+26 x$ $+13 y+15=0$ represents a pair of parallel straight lines, then the distance between them is.........

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Aicharya · Accepted Answer

Given equation is $8 x^2+8 x y+2 y^2+26 x+13 y+15=0$ ...(i) On writing Eq. (i) as quadratic equation in $x$, we get $8 x^2+2 x(4 y+13)+2 y^2+13 y+15=0$ $x=\frac{-2(4 y+13) \pm \sqrt{4(4 y+13)^2-32\left(2 y^2+13 y+15ight.}}{16}$ $\Rightarrow \quad x=\frac{-(4 y+13) \pm 7}{8}$ $\begin{aligned} & \Rightarrow \quad 8 x=-4 y-13+7 	ext { or } 8 x=-4 y-13-7 \ & \Rightarrow \quad 4 x+2 y+3=0 	ext { or } 2 x+y+5=0 \ & \Rightarrow \quad 2 x+y+3 / 2=0 	ext { or } 2 x+y+5=0\end{aligned}$ $	herefore \quad d=\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}ight|$, where, $c_1=5, c_2=3 / 2, a=2, b=1$ $d=\left|\frac{5-3 / 2}{\sqrt{2^2+1^2}}ight|=\frac{7}{2 \sqrt{5}}$

If the equation $8 x^2+8 x y+2 y^2+26 x$ $+13 y+15=0$ represents a pair of parallel straight lines, then the…

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