Mathematics Tes...

There are 3 common tangents of parabola y² = 4x and circle x² + y² – 6x = 0  forming a triangle T. Identify correct facts about triangle 'T'

If length of perpendicular drawn from origin to any normal of the ellipse  is ℓ, then ℓ cannot be –

Points on the ellipse x² + 3y² = 37, where normal is parallel to the line 6x – 5y = 2, is -

The equation  represents

Tangents are drawn to the hyperbola x²/9 - y²/4 = 1, parallel to the straight line 2x – y = 1. The points of contact of the tangents on the hyperbola are

If the maximum area bounded by the curves x² = 4ay, y = ax, y = x/a , 1 < a < 2 is α, then

y = ƒ(x) is differentiable function ∀ x ∈ R and satisfies dy / dx = |y| + 1 and ƒ(0) = 0. 

If a₁, a₂, a₃, a₄, ........., a_n are the solution(s) of equation ƒ(x) = sin²x, then the value of |[a₁] + [a₂] + [a₃] +....... + [a_n]| is not equal to (where [.] denotes greatest integer function)

y = ƒ(x) is differentiable function ∀ x ∈ R and satisfies dy/dx = |y| + 1 and ƒ(0) = 0. 

Which of the following statement is False ?

If locus of the mid point of line segment AB is a conic, then its length of latus rectum is less than

If α = 8, then the equation of line which touches both parabola and ellipse is -