Statement I: An equation of a common tangent to the parabola and the ellipse is…

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Statement I: An equation of a common tangent to the parabola y2=163xy^2 = 16\sqrt{3}x and the ellipse 2x2+y2=42x^2 + y^2 = 4 is y=2x+23y = 2x + 2\sqrt{3} Statement II: If the line y=mx+43my = mx + \frac{4\sqrt{3}}{m}, (m≠0)(m \neq 0) is a common tangent to the parabola y2=163xy^2 = 16\sqrt{3}x and the ellipse 2x2+y2=42x^2 + y^2 = 4 , then mm satisfies m4+2m2=24m^4 + 2m^2 = 24 (1) Statement I is false, statement-II is true (2) Statement I is true, statement-II is true; statement-II is a correct explanation for statement-I (3) Statement I is true, statement II is true; statement II is not a correct explanation for statement I (4) Statement I is true, statement II is false

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