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

Question

The equation 8x2 + 8xy + 2y2 + 26x +13y +15 = 0 represents a pair of straight lines. The distance between them is (A) 7 / √5 (B) 7 / 2√5 (C) √7 / 5 (D) None of these

Tardigrade Admin · Accepted Answer

The distance between the parallel straight lines given by

a x^{2} + 2 h x y + b y^{2} + 2 gx + 2 f y + c = 0

is

2 \frac{g ^{2} - a c}{a ( a + b )}

Here,

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

So, required distance

= 2 \frac{169 - 120}{80} = 2 \times \frac{7}{4 5} = \frac{7}{2 5}

Q. 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

$7/ 5$

$7/2 5$

$7 /5$

None of these

The distance between the parallel straight lines given by
$a x^{2} + 2 h x y + b y^{2} + 2 gx + 2 f y + c = 0$ is $2 \frac{g ^{2} - a c}{a ( a + b )}$
Here, $a = 8, b = 2, c = 15, g = 13.$
So, required distance
$= 2 \frac{169 - 120}{80} = 2 \times \frac{7}{4 5} = \frac{7}{2 5}$

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

7/5​

7/25​

7​/5