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Question

If the curves ax2+4xy+2y2+x+y+5=0 and ax2+6xy+5y2+2x+3y+8=0 intersect at four con-cyclic points then the value of a is

A
4
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B
4
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C
6
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D
6
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Solution

The correct option is B 4
Any second degree curve passing through the intersection of the given curves is
ax2+4xy+2y2+x+y+5+λ(ax2+6xy+5y2+2x+3y+8)=0
If it is a circle, then coefficient of x2= coefficient of y2 and coefficient of xy=0
a(1+λ)=2+5λ and 4+6λ=0
a=2+5λ1+λ and λ=23
a=2+5×23123=2103123=61032=4

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