Given: A circle, 2x² + 2y² = 5 and a parabola, y² = 4 5 x. Statement-1: An equation of a common tangent to these curves is y = x + 5. Statement-2: If the line, y = mx + (5)/m(m ≠ 0) is their common tangent, then m satiesfies m⁴ - 3m² + 2 = 0.

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

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

(C) Statement-1 is true; Statement-2 is false.

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

Coordinate Geometry: JEE Main 2013 Mathematics question

JEE Main 2013 · Session, Shift 1 · Q4678

JEE Main 2013Session, Shift 1MathematicsMediumCoordinate Geometry478× since 2002

Given : A circle,

2{x^2} + 2{y^2} = 5

and a parabola,

{y^2} = 4\sqrt 5 x

. Statement-1 : An equation of a common tangent to these curves is

y = x + \sqrt 5

. Statement-2 : If the line,

y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)

is their common tangent, then

m

satiesfies

{m^4} - 3{m^2} + 2 = 0