Question

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-10 y+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 `Cdot` Statement 2 : If line `L_1` is a a diameter of circle `C ,` then line `L_2` is not a chord of circle `Cdot` Both the statement are True and Statement 2 is the correct explanation of Statement 1. Both the statement are True but Statement 2 is not the correct explanation of Statement 1. Statement 1 is True and Statement 2 is False. Statement 1 is False and Statement 2 is True.
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 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.

Answer 1

Correct Answer - C
Clearly, `x^(2)+y^(2)+6x-10y+30=0` represent a circle having centre at (-3, 5) and radius = 2.
Lines `L_(1)` and `L_(2)` are parallel at a distance of `(6)/(sqrt(13))` units apart.
Clearly, distance between `L_(1)` and `L_(2)` is less than the radius of the circle. So, if `L_(1)` is a chord of the circle, then `L_(2)` is not necessarily a diameter of the circle. Consequently statement-1 is true and statement-2 is false.