For , the circle
and the parabola
intersect in how many distinct points provided
0
2
3
4
The given circle is . Its centre is at
and its radius is 1 . The given parabola is
whose vertex is at
. The circle is symmetrical about the x-axis and the y-axis. The parabola is symmetrical about the y-axis. Since the four points of intersection are distinct, the vertex of the parabola must be outside the circle.
. Also the points of intersection are given by
One root of this equation is positive and the other is negative.
Hence is positive.
Hence
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