Question

10. Problem : Show that the equation 8x² – 24xy +18y2 - 6x +9y - 5= 0 represents a pair of parallel
straight lines and find the distance between them.​

Answer 1

Answer:

A general equation

ax

2

+2hxy+by

2

+2gx+2fy+c=0

represent a straight line which are parallel if;-

h

2

=ab and af

2

=bg

2

and the distance between them is

2

a(a+b)

g

2

−ac

(i)a=8,h=−12,b=18,g=−3,f=

2

9

,c=−5

h

2

=ab=144;af

2

=162=bg

2

So they represent a pair of parallel at lines

Distance=2

8×26

9+40

=

208

14

=

2

13

7

Answer 2

Step-by-step explanation:

Given equation 8x² – 24xy +18y2 - 6x +9y - 5= 0

Compare

a=8,b=18,c=-5,2h=-24 , 2g=-6,. 2f=9

h=-12. g=-3. f=9/2

I. h²=ab=(-12)²=8(18) = 144=144

ii.af²=bg² = 8(9/2)²= 18(-3)² = 8(81/4)=162 = 648/4 =162

162=162

iii. The distance between pair of parallel lines then

=2√g²-ac/a(a+b) = substitute the values in the formula to come the answer