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Question

The distance between the pair of lines represented by the equations x2-6xy+9y2+3x-9y-4=0 is


A

1510

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B

12

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C

52

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D

110

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Solution

The correct option is C

52


Explanation for the correct option:

Finding the distance between the pair of lines:

Given x2-6xy+9y2+3x-9y-4=0

The given equation is of the form ax2+2hxy+by2+2gx+2fy+c=0

Comparing both the equations we get,

a=1,h=-3,b=9,g=32,f=-92,c=-4

The given equation represents a pair of lines,

hence, ∆=0,h2=ab,d=2g2-aba(a+b)

Sice ∆=0, then

abc+2fgh-bg2-af2-ch2=0Substitutingthevaluesweget-36+812-812-814+36=00=0

Thus it satisfies the condition.

Now finding the distance,

d=2g2-aba(a+b)=2322-1×91(1+9)=294-910=29-36410=22540=2254×10=2510=52

The distance between the pair of lines represented by the equations x2-6xy+9y2+3x-9y-4=0 is 52

Hence, option (C) is the correct answer.


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