Ellipse Questions

The locus of the foot of perpendicular drawn from the centre of the ellipse x2 + 3y2 = 6 on any tangent to it is

Equation of the ellipse whose focus is (6,7) directrix is x + y + 2 = 0 and e = 1/ √3 is-

The sum of the squares of the perpendicular on any tangent to the ellipse = 1 from two points on the minor axis each distance from the centre is -...

An ellipse is drawn by taking a diameter of thecircle (x - 1)2 + y2 = 1 as its semi-minor axisand a diameter of the circle x2 + (y - 2)2 = 4as its semi-major axis. If the centre of the ellipseis at th...

The ellipse E1 : = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity ...

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (3, - 1) and has eccentricity is...

The number of values of c such that straight line y = 4x + c touchhes the curve + y2 = 1 is

If a > 2b > 0 then positive value of m for which y = mx - b is a common tangent tox2 + y2 = b2 and (x - a)2 + y2 = b2 is...

The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point (4, 0). Then the equation of the elli...

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is

For the hyperbola = 1, which of the following remains constant when α varies?

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

Area of the greatest rectangle that can be inscribed in the ellipse = 1 is

An ellipse has OB as semi minor axis, F and F′ its focii and the angle FBF′ is a right angle. Then the eccentricity of the ellipse is

The eccentricity of an ellipse, with its centre at the origin, is . If one of the directrices is x = 4, then the equation of the ellipse is...

The foci of the ellipse = 1 and the hyperbola coincide. Then the value of b2 is...

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 9 meets its auxiliary circle at the point M. Then the area of the triangle with v...

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the p...

If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is -

If the eccentricity of an ellipse be 5/8 and the distance between its foci be 10, then its latus rectum is -