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
D.
a hyperbola
The equation of the tangent at any point P(x, y) is
This cuts the coordinate axes at
It is given that P(x, y) is the mid point of AB.
Clearly, it represents a rectangular 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
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