The value of equals:

is equal to‐

equals‐

If , where , then Limitx has the value

The equation of the directrix of the parabola

The equation of the common tangent touching the circle and the parabola above the ‐axis is:

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‐