A hyperbola, having the transverse axis of length , is confocal with the ellipse Then its equation is ‐

The latus rectum of the hyperbola is‐

Statement‐I :: If a point lies in the shaded region , show in the figure, then
Statement‐II :: lies outside the hyperbola , then

Statement‐I The ellipse and are congruent.
Statement‐II The ellipse and have the same eccentricity.

For such questions, we should know properties of ellipse. We should know all the formulas related to ellipse. The axis which is larger is always the major axis.

The minimum area of triangle formed by tangent to the ellipse and coordinate axes‐

An ellipse has OB as semi minor axis, and its focii and the angle FBF’ is a right angle Then the eccentricity of the ellipse is‐

Therefore, the eccentricity of the ellipse is

The number of values of such that the straight line y=4x+c touches the curve is‐

Therefore, there are two values of c.

Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

An ellipse having foci at (3, 3) and (-4,4) and passing through the origin has eccentricity equal to‐

Normals are drawn to parabola from the pointA (h, 0) If triangle ( being the origin) is equilateral, then possible value of h’ is

Given: A circle, and a parabola,
Statement‐I:: An equation of a common tangent to these curves is
Statement‐II:: If the line, is their common tangent, then satisfies

In any equilateral , three circles of radii one are touching to the sides given as in the figure then area of the is

If the sides a, b, c of a triangle are such that a : b : c : : 1 : : 2, then the A : B : C is -

A block placed on a rough inclined plane of inclination ( =30°) can just be pushed upwards by applying a force "F" as shown. If the angle of inclination of the inclined plane is increased to ( = 60°), the same block can just be prevented from sliding down by application of a force of same magnitude. The coefficient of friction between the block and the inclined plane is

The tube AC forms a quarter circle in a vertical plane. The ball B has an area of cross–section slightly smaller than that of the tube, and can move without friction through it. B is placed at A and displaced slightly. It will

A small cube with mass M starts at rest at point 1 at a height 4R, where R is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point 2 is nearly _____ times the cube's weight Mg.