If a circle and the rectangular hyperbola $x y = c^{2}$ meet in the four points whose parameters are $p_{1}, p_{2}, p_{3}$ and $p_{4}$ , then the center of the circle through the points $p_{1}, p_{2}$ and $p_{3}$ is

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Answer the following questions based on the following.C1 and C2 are two circles and points P1,P2,P3,P4,P5 are noted. From which point tangent is possible to C2 but not C1.

The correct option is B P3P3 is on C2 but interior to C1.Hence, it is possible to draw a tangent to C2 but not to C1.So, option B is correct.

Answer the following questions based on the following.
$C_{1}$ and $C_{2}$ are two circles and points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ are noted. From which point tangent is possible to $C_{2}$ but not $C_{1}$ .

The correct option is B $P_{3}$
$P_{3}$ is on $C_{2}$ but interior to $C_{1}$ .
Hence, it is possible to draw a tangent to $C_{2}$ but not to $C_{1}$ .

So, option $B$ is correct.