A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2, then length of semi major axis is
5/3
8/3
2/3
4/3
Equation of the latus rectum of the ellipse 9 x2 + 4 y2 - 18 x - 8 y - 23 = 0 are
y = ± √5
x = ± √5
y = 1 ± √5
x = -1 ± √5
The focal distance of a point P on the parabola y2 = 12 x, if the ordinate of P is 6, is
12
6
3
9
The equation of the latus rectum of the parabola x2 + 4 x + 2 y = 0 is equal to
2 y + 3 = 0
3 y = 2
2 y = 3
3 y + 2 = 0
The equation y2 - 2 y +8 x - 23 = 0 represents.
A pair of straight lines with (1,3) as the common point.
An ellipse with 2 and 4 as semi axes
A parabola with y = 1 as the axis
A parabola with (1,3) as the vertex
The equation of directrix of the ellipse is
3 y = ± 5
y = ± 5
3 y = ± 25
y = ± 3
If distance between directrices of a rectangular hyperbola is 10, then distance between its foci will be
10√2
5
5√2
20
The sum of the distances of a point (2,-3) from the foci of an ellipse 16 (x-2)2 + 25 (y + 3)2 = 400 is
8
50
32
If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latus rectum is
9/2
32/3
64/3
The directrix of the parabola y2 + 4 x + 3 = 0 is
x - 4/3 = 0
x + 1/4 = 0
x - 3/4 = 0
x - 1/4 = 0
