If the line x‐1 =0 is the directrix of the parabola , then one of the values of is :

Assertion (A): Three normals are drawn from the point ’ with slopes to the parabola If locus of ‘ ’ with is a part of the parabola itself then
Reason (R): If normals at and are concurrent then

ABCD and EFGC are squares and the curve passes through the origin and the points and F The ratio is:

Statement‐I :: With respect to a hyperbola pependicular are drawn from a point (5, 0) on the lines , then their feet lie on circle
Statement‐II :: If from any foci of a hyperbola perpendicular are drawn on the asymptotes of the hyperbola then their feet lie on auxiliary circle.

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