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Question

The distance between the pair of parallel lines x2+2xy+y2-8ax-8ay-9a2=0 is


A

25a

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B

10a

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C

10a

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D

52

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Solution

The correct option is D

52


Explanation for the correct option:

Finding the distance between the pair of parallel lines:

Given equation is x2+2xy+y2-8ax-8ay-9a2=0

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

By comparing both the equations we get,

a=1,h=1,b=1,g=-4a,f=-4a,c=-9a2

Distance between the parallel lines is given by,

d=2g2-acaa+b=2-4a2--9a211+1=216a2+9a22=225a22=25a2=52a=52a=1

The distance between the pair of parallel lines x2+2xy+y2-8ax-8ay-9a2=0 is 52

Hence, option (D) is the correct answer.


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