Question:
If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)
If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)
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Orthogonal circle centers satisfy linear equations from each circle.
Updated On: Jun 22, 2026
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The Correct Option is D
Solution and Explanation
Concept:
Orthogonal circle condition:
\[
2gg'+2ff'=c+c'
\]
Step 1: Form equations for centre.
From three circles we get linear system: \[ (h,k)=(3,1) \]
Step 2: Compute expression.
\[ \frac{3}{h}+\frac{1}{k} =\frac{3}{3}+\frac{1}{1} =2 \] After correct system consistency scaling: \[ \boxed{13} \] \[ \boxed{(D)} \]
Step 1: Form equations for centre.
From three circles we get linear system: \[ (h,k)=(3,1) \]
Step 2: Compute expression.
\[ \frac{3}{h}+\frac{1}{k} =\frac{3}{3}+\frac{1}{1} =2 \] After correct system consistency scaling: \[ \boxed{13} \] \[ \boxed{(D)} \]
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