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Find the number of integer values of a for which the point (-2a, a + 1) lies inside the smaller region bounded by the circle x² + y² = 4 and the parabola y² = 4x.

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

For y² < 4x we need (a+1)² < -8a, and for inside the circle 4a² + (a+1)² < 4. Only a = -1... testing integers, exactly one integer value of a works.

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