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Question

Equation of the circle with AB as its diameter is

A
x2+y224x12=0
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B
x2+y2+24x12=0
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C
x2+y212x+24=0
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D
x2+y2+12x+24=0
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Solution

The correct option is C x2+y212x+24=0
The equation of the hyperbola is
x29y24=1
and that of circle is
x2+y28x=0
For their points of intersection
x29+x28x4=1
4x2+9x272x=36
13x272x36=0
13x278x+6x36=0
13x(x6)+6(x6)=0
x=6,x=136
x=136 not acceptable
Now, for x=6,y=±23
Required equation is
(x6)2+(y+23)(y23)=0
x212x+y2+24=0
x2+y212x+24=0

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