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Question

Let x(x - a) + y(y - 1) be a circle. If two chords from (a, 1) bisected by the x-axis are drawn to the circle then the condition required is

A
a2 = 8
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B
a2 < 8
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C
a2 > 8
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D
a=0
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Solution

The correct option is C a2 > 8
The equation of the circle is x2 + y2 -ax -ay = 0
Let (x, 0) be the midpoint of a chord drawn the point (a, 1)
Then the equation of the chord bisected at (x1, 0) is xx192(x+x1)12(y+0)=x21ax1
2x212ax1=2x1xaxax1y.
The chord passes through (a, 1)
2x213ax1+a2+1=0
x1 is real 9a24(2)(a2+1)>0 9a28as8> 0 a2 > 8

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