The circle x² + y² + 2λx = 0, λ  R touches the parabola y² = 4x externally, then -

If b and c are the length of the segments of and focal chord of a parabola y² = 4ax. Then the length of the semi-latus rectum is -

A parabola is drawn with its focus (3, 4) and vertex at the focus of the parabola y² – 12 x – 4y + 4 = 0. The equation of the parabola is -

The range of values of λ for which the point (λ, – 1) is exterior to both the parabola y² = |x| is -

The value of P such that the vertex of y = x² + 2px + 13 is 4 unit above the x axis is -

In the figure, the blocks have unequal masses and . has a downward acceleration a. The pulley P has a radius r, and some mass. The string does not slip on the pulley–

A uniform rod AB of length is free to rotate about a horizontal axis passing through A. The rod is released from rest from horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod :

A thin rod of mass m and length is hinged to a ceiling and it is free to rotate in a vertical plane. A particle of mass m, moving with speed v strikes it as shown in the figure and gets stick with the rod. The value of v , for which the rod becomes horizontal after collision is

An impulsive force F acts horizontally on a solid sphere of radius R placed on a horizontal surface. The line of action of the impulsive force is at a height h above the centre of the sphere. If the rotational and translational kinetic energies of the sphere just after the impulse are equal, then the value of h will be

The disc of radius r is confined to roll without slipping at A and B. If the plates have the velocities shown, then

The figure shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is :

Figure shows a uniform disk, with mass M = 2.4 kg and radius R = 20 cm, mounted on a fixed horizontal axle. A block of mass m = 1.2 kg hangs from a massless cord that is wrapped around the rim of the disk. The tension in cord is

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.