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
= 8
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B
8
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C
8
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D
none
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Solution
The correct option is C 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 xx1−92(x+x1)−12(y+0)=x21−ax1 ⇒2x21−2ax1=2x1x−ax−ax1−y. The chord passes through (a, 1) ⇒2x21−3ax1+a2+1=0 x1 is real ⇒9a2−4(2)(a2+1)>0⇒9a2−8as−8> 0 ⇒a2> 8