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

C_{1}

and

C_{2}

touch each other only at one point

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C_{1}

and

C_{2}

touch each other exactly at two points

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C_{1}

and

C_{2}

intersect (but do not touch) at exactly two points

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C_{1}

and

C_{2}

neither intersect nor touch each other

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Solution

The correct option is B $C_{1}$ and $C_{2}$ touch each other exactly at two points
For points of intersection of circle and parabola, put $y^{2} = 4 x$ in the equation of the circle, we get

$x^{2} + 4 x - 6 x + 1 = 0 o r (x - 1)^{2} = 0$
i.e., they intersect at x = 1.
After substituting in the equation of parabola, we get
$y = 2, - 2$
Thus they touch at the above two points.

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Similar questions

C_{1} : y^{2} = 4 x

C_{2} : x^{2} + y^{2} - 6 x + 1

C_{1} : y^{2} = 4 x

C_{2} : x^{2} + y^{2} - 6 x + 1 = 0

C_{1} : y^{2} = 4 x, C_{2} : x^{2} + y^{2} - 6 x + 1 = 0

C_{1} : y^{2} = 4 x, C_{2} : x^{2} + y^{2} - 6 x + 1 = 0.

C_{1} \equiv x^{2} + y^{2} - 4 = 0

C_{2} \equiv x^{2} + y^{2} - 6 x + 8 = 0

C_{3} \equiv x^{2} + y^{2} - 8 x - 2 y + 16 = 0

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