jee-advanced 2008 Q1

jee-advanced · India · paper1 Circles Intersection of Circles or Circle with Conic
Consider the two curves $$\begin{aligned} & C _ { 1 } : y ^ { 2 } = 4 x \\ & C _ { 2 } : x ^ { 2 } + y ^ { 2 } - 6 x + 1 = 0 \end{aligned}$$ Then,
(A) $C _ { 1 }$ and $C _ { 2 }$ touch each other only at one point
(B) $C _ { 1 }$ and $C _ { 2 }$ touch each other exactly at two points
(C) $C _ { 1 }$ and $C _ { 2 }$ intersect (but do not touch) at exactly two points
(D) $C _ { 1 }$ and $C _ { 2 }$ neither intersect nor touch each other
Consider the two curves
$$\begin{aligned}
& C _ { 1 } : y ^ { 2 } = 4 x \\
& C _ { 2 } : x ^ { 2 } + y ^ { 2 } - 6 x + 1 = 0
\end{aligned}$$
Then,\\
(A) $C _ { 1 }$ and $C _ { 2 }$ touch each other only at one point\\
(B) $C _ { 1 }$ and $C _ { 2 }$ touch each other exactly at two points\\
(C) $C _ { 1 }$ and $C _ { 2 }$ intersect (but do not touch) at exactly two points\\
(D) $C _ { 1 }$ and $C _ { 2 }$ neither intersect nor touch each other