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Question

The equation of the circle passing through the origin and the points of intersection of the circles x2+y2−4x−6y−3=0, x2+y2+4x−2y−4=0

A
x2+y2+28x+18y=0
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B
x2+y218x28y=0
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C
x2+y228x+18y=0
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D
x2+y228x18y=0
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Solution

The correct option is D x2+y228x18y=0

By family of circles,
equation of circle passing through point of intersection
of s1:x2+y24x6y3=0 and s2:x2+y2+4x2y4=0 is
s1+λs2=0
(1+λ)x2+(1+λ)y2+4(λ1)x2(3+λ)y34λ=0
Given this circles pass through origin (0,0)
34λ=0
λ=34
Equation of circle is
x24+y2428x418y4=0
x2+y228x18y=0


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