STATEMENT-1: An equation of a common tangent to the parabola y² = 16 3 x and the ellipse 2x² + y² = 4 is y = 2x + 2 3 STATEMENT-2:If line y = mx + (4 3)/m,(m ≠ 0) is a common tangent to the parabola y² = 16√(3x) and the ellipse 2x² + y² = 4, then m satisfies m⁴ + 2m² = 24

(B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(A) Statement-1 is false, Statement-2 is true.

(C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(D) Statement-1 is true, Statement-2 is false.

Coordinate Geometry: JEE Main 2012 Mathematics question

JEE Main 2012 · Annual, Paper 1 · Q3719

JEE Main 2012Annual, Paper 1MathematicsHardCoordinate Geometry478× since 2002

STATEMENT-1 : An equation of a common tangent to the parabola

{y^2} = 16\sqrt 3 x

and the ellipse

2{x^2} + {y^2} = 4

y = 2x + 2\sqrt 3

STATEMENT-2 :If line

y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)

is a common tangent to the parabola

{y^2} = 16\sqrt {3x}

and the ellipse

2{x^2} + {y^2} = 4

, then

m

satisfies

{m^4} + 2{m^2} = 24

JEE Main 2012 · Annual, Paper 1 · Q3719

JEE Main 2012Annual, Paper 1MathematicsHardCoordinate Geometry478× since 2002

STATEMENT-1 : An equation of a common tangent to the parabola

{y^2} = 16\sqrt 3 x

and the ellipse

2{x^2} + {y^2} = 4

y = 2x + 2\sqrt 3

STATEMENT-2 :If line

y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)

is a common tangent to the parabola

{y^2} = 16\sqrt {3x}

and the ellipse

2{x^2} + {y^2} = 4

, then

m

satisfies

{m^4} + 2{m^2} = 24