    Question

# The circle x2+y2−8x=0 and hyperbola x29−y24=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+y2−12x+24=0 The equation of the hyperbola is x29−y24=1 and that of circle is x2+y2−8x=0 For their points of intersection , x29+x2−8x4=1 ⇒4x2+9x2−72x=36 ⇒13x2−72x−36=0 ⇒13x2−78x+6x−36=0 ⇒13x(x−6)+6(x−6)=0 ⇒x=6,x=−136 x=−136 not acceptable. Now, for x=6,y=±2√3 Required equation is, (x−6)2+(y+2√3)(y−2√3)=0 ⇒x2−12x+y2+24=0 ⇒x2+y2−12x+24=0  Suggest Corrections  0      Similar questions  Related Videos   Hyperbola and Terminologies
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