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If $x^{2} + y^{2} + 4 x + 8 y = 5$ is a circle, then match the following

COLUMN : I

COLUMN : II
A
If $(α, β)$ is the center of the circle then the value of $| α + β |$ is
P
6
B
The radius of the circle is
Q
5
C
If the equation of tangent to the circle at the point $P (1, - 8)$ is $a x - 4 y + c = 0$ then the value of $12 a + c$ is
R
1
D
If the equation of normal to the circle at the point $P (- 5, 0)$ is $4 x + b y + c = 0$ then the value of $11 b - c$ is
S
13

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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 A.

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Detailed Solution

Centre $(- g, - f)$ radius is $\sqrt{g^{2} + f^{2} - c}$ , tangent:
$x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c = 0$

Normal: $(x_{1} + g) (y - y_{1}) = (y_{1} + f) (x - x_{1})$

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