If the normal at one end of the latusrectum of an ellipse passes through the one end of the minor axis, then
e4 - e2 + 1 = 0
e2 - e + 1 = 0
e2 + e + 1 = 0
e4 + e2 - 1 = 0
The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is
a parabola
an ellipse
a circle
a hyperbola
The combined equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 + 4x + 5y = 0 is
2x2 + 5xy + 2y2 + 4x + 5y - 2 = 0
2x2 + 5xy + 2y2 = 0
2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0
None of the above
A point on the ellipse : at a distance equal to the mean of length of the semi-major and semi-minor axes from the centre, is
D.
Let P() be a point on the given ellipse such that its distance from the centre (0, 0) of the ellipse is equal to the mean of the lengths of the semi-major and semi-minor axes, i.e.
Hence, the required points are given by,
The parametric coordinates of any point on the parabola whose focus is (0, 1) and the directrix is x + 2 = 0, are
(t2 - 1, 2t + 1)
(t2 + 1, 2t + 1)
(t2, 2t)
(t2 + 1, 2t - 1)
The normal at the point (, 2at1) on the parabola meets the parabola again in the point (), then
If the rectangular hyperbola is x2 - y2 = 64. Then, which of the following is not correct?
The length of latusrectum is 16
The eccentricity is
The asymptotes are parallel to each other
The directrices are x =
The equation of tangents to the hyperbola 3x2 - 2y2 = 6, which is perpendicular to the line x - 3y = 3, are