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Question

If the circles (x+a)2+(y+b)2=a2, (x+α)2+(y+β)2=β2
cut orthogonally then α2+b2=

A
aα+bβ
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B
a2+β2
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C
2(aα+bβ)
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D
2(aα+bβ)
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Solution

The correct option is C 2(aα+bβ)
If two circle cut orthogonally then,
r21+r22=(c1c2)2
(x+a)2+(y+b)2=a2
r1=a and c1=(a,b)
and (x+α)2+(y+β)2=β2
r2=β and c2=(α,β)
a2+β2=a2+α2=2αa+β2+b22bβ
α2+β2=2(αa+βb)

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