Question

Consider the two curves

$C_1:y^2=4x$
$C_2:x^2+y^2-6x+1=0$

Which of the following is true?

• 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 $C_2$ intresect (but do not touch) at exactly at two points
• D. $C_1$ and $C_2$ neither intersect nor touch each other

Answer 1

The correct option is B $C_1$ and $C_2$ touch each other exactly at two points

Solving both the curves $x^2+4x-6x+1=0\Rightarrow (x-1{)}^2=0\Rightarrow x=1$
$\Rightarrow y^2=4\left(1\right)\Rightarrow y=\pm 2$
Hence both the curves will touch at two points.