Match List-I with List-II and select the correct answer using the code given below the list. List - I List - II (P) The centre of the circle with least radius passing through ( 1 , 1 ) and ( 3 , 3 ) i

Question

Match List-I with List-II and select the correct answer using the code given below the list.

List - I	List - II
(P) The centre of the circle with least radius passing through $(1, 1)$ and $(3, 3)$ is $(p, q)$ , then $(p + q)$ is	(1) 1
(Q) A circle touching both axes and whose centre lies on the line x $- 2 y = 3$ and in fourth quadrant is ( $p, q$ ), then ( $p + q$ ) is	(2) 4
(R) Equation of the circle touching x -axis at origin and passing through $(1, 2)$ is $x^{2} + y^{2} - λ y = 0$ , then $2 λ$ is	(3) 0
(S) If $x^{2} + y^{2} - 4 x + 3 = 0$ , then minimum value of $x^{2} + y^{2}$ is	(4) 5
	(5) 2

TestHub · Accepted Answer

(P) centre is ( 2 , 2 ) ⇒ p + q = 4 (Q) Let C(3 + 2y, y) ​ ∣ y ∣ = ∣3 + 2 y ∣ ​ y = − 1 ⇒ x = 1 ​ ⇒ p + q = 0 ​ (R) CP = b ​ 1 + ( b − 2 ) 2 = b 2 ​ 1 + 4 − 4 b = 0 ​ b = 4 5 ​ ​ \end{center} ⇒ equation of circle is x 2 + y 2 − 2 5 ​ y = 0 ⇒ λ = 2 5 ​ ⇒ 2 λ = 5 ​ (S) x = 2 + cos θ ​ y = sin θ ​ ⇒ x 2 + y 2 = 4 x − 3 ​ = 4 cos θ + 5 ≥ 1

Mathematics - Circle Question with Solution | TestHub

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