A small block of mass 'm' is rigidly attached at 'P' to a ring of mass '3m' and radius 'r'. The system is released from rest at and rolls without sliding. The angular acceleration of hoop just after release is

x – 2 = t², y = 2t are the parametric equations of the parabola

parametric form gives us the general coordinates of the curve. we can solve for the two to build the relationship between the x and y coordinates which gives us the locus

Vertex of the parabola y² + 2y + x = 0 lies in the quadrant

vertex of the parabola is the point that divides the curve into two symmetric parts.

The equation of the parabola with focus (3, 0) and the directrix x + 3 = 0 is

the locus of all points which are equidistant from a point called focus and a aline called directrix is known as a parabola. as per this definition, we can solve the  given question.

Length of the shortest normal chord of the parabola y² = 4x is-

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x₁, y₁) and (x₂, y₂) respectively, then-

The common tangents to the circle x² + y² = a²/2 and the parabola y² = 4ax intersect at the focus of the parabola-

If on a given base triangle b be described such that the sum of the tangents of the base angles is constant (k), then the locus of third vertex is -

Set of values of ‘h’ for which the number of distinct common normals of (x – 2)² = 4(y – 3) and x² + y² – 2x – hy – c = 0 (c > 0) is 3, is -

PA and PB are the tangents drawn to y² = 4x from point P. These tangents meet the y-axis at the points A₁ and B₁ respectively. If the area of triangle PA₁ B₁ is 2 sq. units, then locus of ‘p’ is -

If the chord of contact of tangents from a point P to the parabola y² = 4ax, touches the parabola x² = 4by, then the locus of P is a/an -

AB, AC are tangents to a parabola y² = 4ax. If l₁, l₂, l₃ are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then -

Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x² – 4x + 6y + 10 = 0, will touch a fixed line whose equation is -

AB is a double ordinate of the parabola y² = 4ax. Tangents drawn to parabola at A and B meets y-axis at A₁ and B₁ respectively. If the area of trapezium AA₁ B₁ B is equal to 12a², then angle subtended by A₁B₁ at the focus of the parabola is equal to -

The parabola y² = 4x and the circle (x – 6)² + y² = r² will have no common tangent, if ‘r’ is equal to -

The name of the conic represented by the equation x² + y² – 2xy + 20x + 10 = 0 is-