Parabola

If the line lx + my + n = 0 touches the parabola y² = 4ax, then

(a)   In = am

(b)  In² = am²

(c)  l²n = am²

(d)   In = am²

x=t²+ 1 & y = 2t +1. Tha cartesian equation of its directrix is

In general, three normals can be drawn through a point in the plane of a parabola to the curve.

The equation of the ellipse having foci (2, 0), ( -2, 0) and minor axis of length 8 units is:

If L ≡ x + y – 1 = 0 is a line and S ≡ y – x + x² = 0 is a parabola, then which of the following is true?

(A)   L = 0 and S = 0 do not have common points

(B)   L = 0 cuts S = 0 in two distinct points

(C)   L = 0 touches the parabola S = 0

(D)   L = 0 is the directrix of the parabola S = 0 

Show that the locus of the midpoints of chords of a parabola passing through the vertex is in turn a parabola whose latus rectum is half of the latus rectum of the original. 

Let L be the point (t, 2) and M be a point on the y-axis such that the slope of LM is −t. Then, the locus of the midpoint of LM is a parabola whose latus rectum is

(a)  2

(b)   1/2

(c)   4

(d)  1/4

Determine the coordinates of the focus, the equation of the directrix and the length of the latus rectum of the parabola

y² = (8/3)x.

A point P of the parabola y² = 4ax lies on the line y = x. The normal chord PQ, normal at P, subtends an angle at the focus of the parabola which equal

(A)  60º

(B)  45º

(C) 30º

(D)  90º