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Given : A circle, 2x² + 2y² = 5 and a parabola, y² = 4√5x. Statement - I : An equation of a common tangent to these curves is y = x + √5. Statement - II : If the line, y = mx + √5/(m ≠ 0) is their common tangent, then m satisfies m⁴ − 3m² + 2 = 0.

1. Statement - I is true, Statement - II is false
2. Statement - I is false, Statement - II is true
3. Both Statement - I and Statement - II are true
4. Both Statement - I and Statement - II are false

Correct answer: Both Statement - I and Statement - II are false

Solution

Both statements are incorrect because the proposed tangent line does not satisfy the conditions for tangency to either the circle or the parabola. For a line to be a common tangent, it must touch both curves at exactly one point, which is not the case here.

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