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(#M40021777) IIT-JEE question statement type Keep an EYE

Consider
L1 : 2x + 3y + p - 3 = 0
L2 : 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 L1 is a chord of circle C, then line L2 is not always a diameter of circle C.
and
STATEMENT -2 : If line L1 is a diameter of circle C, then line L2 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 False
(D) STATEMENT -1 is False, STATEMENT -2 is True

Asked In IIT-JEE MAN (12 years ago)

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sameer sharma  (6 years ago)

L1: 2x+3y+p-3=0

L2: 2x+3y+p+3=0

C: x2+y2+6x-10y+30=0, => C(-3, 5),

If L1 is the chord of C then


for L2 to be diameter

2(-3)+3(5)+p+3=0 => p = -12

hence statement 1 is true

as p = -12 lies in the range [L2 is dia only if p = -12]

statement-2:

if L1 is dia then

2(-3)+3(5)+p-3=0 => p = -6

if L2 is the chord then


p = -6 does not imply that L2 cannot be the chord of circle

hence statement 2 is false

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