Match the items of List I with items of List II and choose the correct option. List –I List –II(I)Q is image of P(2, 4) in bisector line L of 1st quadrant, S is circle with centre Q and radius 4. A circle M is drawn such that it touch line L at (1, 1) and its radical axis with S passes through P then its radius is (P)122(II)Tangents are drawn from P(K, 0) on x2+y2=50, meeting y –axis at Q & R possible value of K for which area of ΔPQR is minimum.(Q)50(III)If length of major axis of ellipse 2x2+xy+y2=5, is 2k and k2 = 10a−b, then a2b is : (a is integer) (R)1622(IV)Centre of a circle passing through foci of x225−y224=1 and through the point of intersection of tangents at vertices with tangent at point (52,26) is (h, k) then |2. 3k| equal(S)10 (T)162

Question

Match the items of List I with items of List II and choose the correct option. List –I List –II(I)Q is image of  P(2, 4) in bisector line L of 1st  quadrant, S is circle with centre Q and radius 4. A circle M is drawn such that it touch line L at (1, 1) and its radical axis with S passes through P then its radius is (P)122(II)Tangents are drawn from P(K, 0) on  x2+y2=50, meeting y –axis at Q & R possible value of K for which area of  ΔPQR  is minimum.(Q)50(III)If  length of major axis of ellipse  2x2+xy+y2=5, is  2k and k2 = 10a−b, then  a2b  is : (a is integer) (R)1622(IV)Centre of a circle passing through foci of  x225−y224=1 and through the point of intersection of tangents at vertices with tangent at point  (52,26)  is (h, k) then |2. 3k| equal(S)10  (T)162

Infinity Learn · Accepted Answer

$I \to Q; I I \to S; I I I \to S; I V \to P$

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	List –I		List –II
(I)	Q is image of P(2, 4) in bisector line L of 1^st quadrant, S is circle with centre Q and radius 4. A circle M is drawn such that it touch line L at (1, 1) and its radical axis with S passes through P then its radius is	(P)	$12 \sqrt{2}$
(II)	Tangents are drawn from P(K, 0) on $x^{2} + y^{2} = 50$ , meeting y –axis at Q & R possible value of K for which area of $Δ P Q R$ is minimum.	(Q)	$\sqrt{50}$
(III)	If length of major axis of ellipse $2 x^{2} + x y + y^{2} = 5$ , is 2k and $k^{2}$ = $\frac{10}{a - b}$ , then $a^{2} b$ is : (a is integer)	(R)	$\frac{\sqrt{162}}{2}$
(IV)	Centre of a circle passing through foci of $\frac{x^{2}}{25} - \frac{y^{2}}{24}$ =1 and through the point of intersection of tangents at vertices with tangent at point $(5 \sqrt{2}, 2 \sqrt{6})$ is (h, k) then \|2. $\sqrt{3}$ k\| equal	(S)	$10$
		(T)	$\sqrt{162}$