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 C2(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+b2−2bβ ⇒α2+β2=2(αa+βb)