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Let y² = 4ax be a parabola and x² + y² + 2bx = 0 be a circle. If the parabola and circle touch each other externally, then which condition holds?

1. a > 0, b > 0
2. a > 0, b < 0
3. a < 0, b > 0
4. a < 0, b < 0

Correct answer: a > 0, b > 0

Solution

The parabola opens rightward for a > 0; the circle has centre (-b,0) passing through the origin, lying in the left half for b > 0. They touch externally at the origin when a > 0 and b > 0.

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