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Standard XI

Mathematics

Condition for Two Lines to Be Parallel

The equation ...

Question

The equation $8 x^{2} + 8 x y + 2 y^{2} + 26 x + 13 y + 15 = 0$ represents a pair of straight lines.The distance between them is

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Solution

The correct option is B

The distance between the parallel straight lines given by $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ is $2 \sqrt{\frac{g^{2} - a c}{a (a + b)}}$ .

Here, a = 8, b= 2 , c= 15, g = 13.

So, required distance = $2 \sqrt{\frac{169 - 120}{80}} = \frac{7}{2 \sqrt{5}} .$

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The equation 8x2+8xy+2y2+26x+13y+15=0 represents a pair of straight lines.The distance between them is

The correct option is B The distance between the parallel straight lines given by ax2+2hxy+by2+2gx+2fy+c=0 is 2√g2−aca(a+b). Here, a = 8, b= 2 , c= 15, g = 13. So, required distance = 2√169−12080=72√5.

The equation $8 x^{2} + 8 x y + 2 y^{2} + 26 x + 13 y + 15 = 0$ represents a pair of straight lines.The distance between them is