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Question

The circle x2+y28x=0 and hyperbola x29y24=1 intersect at the points A and B.
Equation of the circle with AB as its diameter is


A

x2+y212x+24=0

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B

x2+y2+12x+24=0

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C

x2+y2+24x+12=0

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D

x2+y224x12=0

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Solution

The correct option is A

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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