jee-advanced 2008 Q12

jee-advanced · India · paper2 Circles Chord Length and Chord Properties
Consider
$$\begin{aligned} & L _ { 1 } : 2 x + 3 y + p - 3 = 0 \\ & L _ { 2 } : 2 x + 3 y + p + 3 = 0 \end{aligned}$$
where $p$ is a real number, and $C : x ^ { 2 } + y ^ { 2 } + 6 x - 10 y + 30 = 0$. STATEMENT-1 : If line $L _ { 1 }$ is a chord of circle $C$, then line $L _ { 2 }$ is not always a diameter of circle $C$.
and
STATEMENT-2 : If line $L _ { 1 }$ is a diameter of circle $C$, then line $L _ { 2 }$ is not a chord of circle $C$.
(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
Consider

$$\begin{aligned}
& L _ { 1 } : 2 x + 3 y + p - 3 = 0 \\
& L _ { 2 } : 2 x + 3 y + p + 3 = 0
\end{aligned}$$

where $p$ is a real number, and $C : x ^ { 2 } + y ^ { 2 } + 6 x - 10 y + 30 = 0$.\\
STATEMENT-1 : If line $L _ { 1 }$ is a chord of circle $C$, then line $L _ { 2 }$ is not always a diameter of circle $C$.

and

STATEMENT-2 : If line $L _ { 1 }$ is a diameter of circle $C$, then line $L _ { 2 }$ is not a chord of circle $C$.\\
(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