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Question

Equation 6x25xy+y2=0 represents____________________


A

Pair of coincident lines

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B

Pair of imaginary lines with real point of intersection i.e.(0,0)

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C

Pair of distinct straight lines

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D

None of these

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Solution

The correct option is C

Pair of distinct straight lines


Given equation is a homogeneous equation of second degree so, it represents a pair of straight line passing through origin.

Comparing the equation with ax2+2hxy+by2=0

We obtain a=6, b=1, h= 52

h2ab=2546=14

h2ab>0h2>ab

h2>ab

Hence, given equation represents a pair of distinct straight lines passing through the origin.

Option C is correct.


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