IIT-JEE
Exam
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
Read Solution (Total 1)
-
- 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 - 5 years agoHelpfull: Yes(0) No(0)
IIT-JEE Other Question
A particle P starts from the point z0 = 1 + 2i, where i = -1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves 2 units in the direction of the vector i + j and then it moves through an angle 2i in anticlockwise direction on a circle with centre at origin, to reach a point z2. The point z2 is given by
Let a, b, c, p, q be real numbers. Suppose i i^2 are the roots of the equation x^2 + 2px + q = 0 and i, 1i^2 are the roots of the equation ax^2 + 2bx + c = 0, where i^2 = {-1, 0, 1}.
STATEMENT -1 : (p^2 - q) (b^2 - ac) = 0
and
STATEMENT -2 : b = pa or c = qa
(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