AP EAMCET2010MathematicsStraight Lines

The distance between the two lines represented by 8 x^2-24 x y+18 y^2-6 x+9 y-5=0 is

Options

A0
B3 4 13
C6 13
D7 2 13

Correct answer

D. 7 2 13

Step-by-step solution

The given equation of family of lines 8 x^2-24 x y+18 y^2-6 x+9 y-5=0 (i) Comparing with a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 Then, array c a=8, h=-12, b=18 g=-3, f=9 / 2, c=-5 array . We know that, the distance between two lines represented by 8 x^2-24 x y+18 y^2-6 x+9 y-5=0 is 2 [ (g^2-a c ) a(a+b) ] =2 9+40 8(8+18) =2 49 208 = 7 52 = 7 2 13

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