The equation of the directrix of the parabola x2 = -4ay is.
x + a = 0
x - a = 0
y + a = 0
y - a = 0
The locus of the points which are equidistance from (-a , 0) and x = a is
y2 = 4ax
y2 = -4ax
x2 + 4ay = 0
x2 - 4ay = 0
If the line 2x - 3y + 6 = 0 is a tangent to the parabola y2 = 4 ax , then a is equal to
4/3
3/4
-4/3
-7/4
The equation x = at2, y = 2 at: t∈ R represent
A circle
An ellipse
A hyperbola
A parabola
The tangents at the points (at21, 2at1), (at22, 2at2) on the parabola y2 = 4ax are at right angles if
t1t2 = -1
t1t2 =1
t1t2 = 2
t1t2 = -2
The equation of the parabola with focus at (0, 3) and the directrix y + 3 = 0 is.
y2 = 12 x
y2 = -12 x
x2 = 12 y
x2 = -12 y
The vertex of the parabola y2 + 6x - 2y + 13 = 0 is
(1, -1)
(-2, 1)
(3/2, 1)
(-7/2 ,1)
A line touches the circle x2 + y2 = 2 a2 and also the parabola y2 = 8 ax.Its equation is
y = ± x
y = ± (x + c)
y = ±( x + 2a)
y = ± ( x - 2a)
The point on the parabola y2 = 8x whose distance from the focus is 8, has x co-ordinate as
0
2
4
6
The vertex of the parabola y2 = 4a (x - a) is
(a, 0)
(0, a)
(0, 0)
None of these
