Ellipse Questions

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

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

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

Number of points on the ellipse = 1 from which pair of perpendicular tangents are drawn to the ellipse = 1 is :-...

Maximum length of chord of the ellipse = 1, such that eccentric angles of its extremities differ by is -...

If the eccentricity of the hyperbola x2 - y2 sec2θ = 4 is √3 times the eccentricity of the ellipse x2sec2θ + y2 = 16, then the value of θ equals to :-...

The foci of a hyperbola lie at the vertices of the ellipse = 1 and its directrixes pass through the foci of the ellipse. The equation of the hyperbola must be :-...

Area of the ellipse (2x + 3y - 5)2 + 4(-3x + 2y + 1)2 = 52 is equal to-

The equation to the ellipse (referred to its axes as the axes of x and y respectively) whose foci are (± 2, 0) and eccentricity 1/2,is-

The eccentricity of the ellipse 9x2 + 5y2 − 30 y = 0 is-