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GMAT Problem Solving (PS) | How many points with Integer x and Y co-ordinates lie within the circl

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How many points with Integer x and Y co-ordinates lie within the circle with centre at origin if the circle intersects with parabola y = ax^2 + 4 where a>0 at only one Point

Circle touches parabola at only 1 point.

So, that means they just touch each other. For the parabola, if x=0, y=4. So the parabola intersects the y-axis at (0,4).

This is the point where circle touched the parabola. Even if 'a' is any value > 0.

Circle of circle is given as (0,0). Now, we have got the circle with
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