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Equation of a Chord with a Given Middle Point

If the circle...

Question

If the circle $| z - 1 | = 3$ and $| z - z_{o} | = 3$ intersect orthogonaly, then?

| z_{o} | \geq 3

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3 \leq | z_{o} | \leq 5

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4 \leq | z_{o} | \leq 6

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2 \leq | z_{o} | \leq 3

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Solution

The correct option is D $2 \leq | z_{o} | \leq 3$
For $| z - 1 | = 3 & | z - z_{0} | = 3$ to intersect orthogonally, $z_{0}$ should lie on the circle $| z - 3 | = 3$
$∴ 2 \leq | z_{0} | \leq 3$
Hence, the answer is $2 \leq | z_{0} | \leq 3.$

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