From the point P(4, –4) tangents PA and PB are drawn to the circle $x^{2} + y^{2} - 6 x + 2 y + 5 = 0$ whose centre is C then match the following
COLUMN - I COLUMN - II
(A) Length of AB p) 5/2
(B) Tangent of the angle between PA and PC q) $\sqrt{10}$
(C) Area of triangle PAB r) 1
(D) Absolute difference of slopes of PA and PB s) 3/4
A B C D
1) q r p p
2) r q p p
3) p r q p
4) q q r p

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Detailed Solution

A) length of chord of contact

$AB = \frac{2 r \sqrt{S_{11}}}{\sqrt{S_{11} + r^{2}}} = \frac{2 \sqrt{5} \sqrt{5}}{\sqrt{10}} = \sqrt{10}$

B) $\tan θ / 2 = \frac{r}{\sqrt{S_{11}}} = \frac{\sqrt{5}}{\sqrt{5}} = 1$

C) Area of Ole $= \frac{{rS}_{11}^{3 / 2}}{S_{11} + r^{2}} = \frac{5}{2}$

D) Let $\overset{\leftrightarrow}{PA} be y + 4 = m (x - 4); r = d \Rightarrow m = 2 or \frac{- 1}{2}$

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COLUMN - I		COLUMN - II
(A)	Length of AB	p)	5/2
(B)	Tangent of the angle between PA and PC	q)	$\sqrt{10}$
(C)	Area of triangle PAB	r)	1
(D)	Absolute difference of slopes of PA and PB	s)	3/4