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If $x^{2} + y^{2} + 22 x = 4 y + 100$ and $x^{2} + y^{2} + 4 y + 100 = 22 x$ represents two circles
Then match the following

COLUMN : I

COLUMN : II
A
If $r_{1}$ and $r_{2}$ are the radii of the two circles then the value of $| \frac{r_{1} + r_{2}}{r_{1} - r_{2}} |$ is
P
10
B
If $r_{1}$ and $r_{2}$ are the radii of the two circles and the distance between the centers of the circles is d then the value of $\sqrt{d^{2} - {(r_{1} + r_{2})}^{2}}$ is
Q
2
C
If $r_{1}$ and $r_{2}$ are the radii of the two circles and the distance between the centers of the circles is d then the value of $\sqrt{d^{2} - {(r_{1} - r_{2})}^{2}}$ is
R
5
D
If $A_{1}$ and $A_{2}$ are the areas of the two circles then the value of $4 | \frac{A_{1} + A_{2}}{A_{1} - A_{2}} |$ is
S
20

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$A \to Q, B \to P, C \to S, D \to R$

$A \to P, B \to Q, C \to R, D \to S$

$A \to R, B \to S, C \to P, D \to Q$

$A \to S, B \to R, C \to Q, D \to P$

answer is C.

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Detailed Solution

$r^{2} = g^{2} + f^{2} - c, {(g_{1} - g_{2})}^{2} + {(f_{1} - f_{2})}^{2}$

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