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Q.
The equation $8x^2 + 8xy + 2y^2 + 26x +13y +15 = 0$ represents a pair of straight lines. The distance between them is
Straight Lines
Solution:
The distance between the parallel straight lines given by
$ax^{2}+2hxy+by^{2}+2\,gx+2\,fy+c=0$ is $2\sqrt{\frac{g^{2}-ac}{a\left(a+b\right)}}$
Here, $a = 8, b = 2, c = 15, g = 13.$
So, required distance
$=2\sqrt{\frac{169-120}{80}}=2\times\frac{7}{4\sqrt{5}}=\frac{7}{2\sqrt{5}}$