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The parabola y^2 = 4x and the circle ...

The parabola `y^2 = 4x` and the circle `x^2 + y^2 - 6x + 1=0`

A

intersect at exactly one point

B

touch each other at two distinct points

C

touch each other at exactly one point

D

intersect at two distinct points

Text Solution

Verified by Experts

The correct Answer is:
D
The parabola `y^(2)=4x` and the circle `x^(2)+y^(2)-6x+1=0` will intersect, if `x^(2)+4x-6x+1=0`
`implies(x^(2)-2x+1)=0`
`implies" "(x-1)^(2)=0impliesx=1,1`
`:." "y=sqrt(4)=+-2`
So, intersecting points are (1, -2) and (1, 2).
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 14-Paper 2 (Mathematics)
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