Mathematics

Problem

Statement I: An equation of a common tangent to the parabola

y^2 = 16\sqrt{3}x

and the ellipse

2x^2 + y^2 = 4

y = 2x + 2\sqrt{3}

Statement II: If the line

y = mx + \frac{4\sqrt{3}}{m}

(m \neq 0)

is a common tangent to the parabola

y^2 = 16\sqrt{3}x

and the ellipse

2x^2 + y^2 = 4

, then

m

satisfies

m^4 + 2m^2 = 24

a. Statement I is false, statement-II is true b. Statement I is true, statement-II is true; statement-II is a correct explanation for statement-I c. Statement I is true, statement II is true; statement II is not a correct explanation for statement I d. Statement I is true, statement II is false

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