Question

5. Find the distances between the following pairs of parallel straight lines:
9x2 - 6xy + y2 + 18x - 6y + 8 = 0
THI + 23 n + 3y - 3x - 3y3y-4 = 0,​

Answer 1

S≡9x

2

−6xy+y

2

+18x−6y+8=0

This equation is of the form :

S≡ax

2

+2hxy+by

2

+2gx+2fy+C=0 _____ (A)

Reverting the main equation

S≡9x

2

+2(−3)xy+(1)y

2

+2(9)x+2(−3)y+8=0

Compairing this equation with equation (A), we get

a=9;b=1;c=8;h=−3;g=9;f=−3

Distance between two parallel lines is given by :

d=2

a(a+b)

g

2

−ac

or d=2

b(a+b)

f

2

−bc

So, d=2

a(a+b)

9

2

−ac

=2

a(a+1)

(9)

2

−9(8)

=2

9×10

81−72

=2

9×10

9

⇒d=

10

2