Consider L_1 : 2x + 3y + p - 3 = 0 L_2 : 2x + 3y + p + 3 = 0, where p is a real number, and C : x^2 + y^2 + 6x - 10y + 30 = 0. STATEMENT-1 : If line L_1 is a chord of circle C, then line L_2 is not always a diameter of circle C. and STATEMENT-2 : If line L_1 is a diameter of circle C, then line L_2 is not a chord of circle C.

JEE Advanced 2008 Mathematics question

Consider

: 2x + 3y + p - 3 = 0

: 2x + 3y + p + 3 = 0,

where p is a real number, and . STATEMENT-1 : If line is a chord of circle C, then line is not always a diameter of circle C. and STATEMENT-2 : If line is a diameter of circle C, then line is not a chord of circle C.

(A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
(B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
(C)STATEMENT-1 is True, STATEMENT-2 is FalseCorrect
(D)STATEMENT-1 is False, STATEMENT-2 is True

Answer: (C)

Solution

C has centre (−3, 5) and radius . The parallel lines , are apart. Statement-1: can be a chord for a range of p, and is a diameter only for the single value p =

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Question ID VK-037616