Consider the two curves C_1: y^2=4 x, C_2: x^2+y^2-6 x+1=0. Then, - Vidyadip

MCQ

Consider the two curves $C_1: y^2=4 x, C_2: x^2+y^2-6 x+1=0$. Then,

A
$\mathrm{C}_1$ and $\mathrm{C}_2$ touch each other only at one point
✓
$\mathrm{C}_1$ and $\mathrm{C}_2$ touch each other exactly at two points
C
$\mathrm{C}_1$ and $\mathrm{C}_2$ intersect (but do not touch) at exactly two points
D
$\mathrm{C}_1$ and $\mathrm{C}_2$ neither intersect nor touch each other

✓

Answer

Correct option: B.

$\mathrm{C}_1$ and $\mathrm{C}_2$ touch each other exactly at two points

b
The circle and the parabola touch each other at $x=1$ $ei.e$. at the points $(1,2)$ and $(1,-2)$ as shown in the figure.

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