An ellipse passing through the origin has its foci (3, 4) and (6, 8). The length of its semi-minor axis is `bdot` Then the value of `b/(sqrt(2))` is____

Find the equation of the ellipse whose foci are (2, 3) and (-2, 3) and whose length of semi minor axis is sqrt5

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

Find the equation of the ellipse whose foci are (2,3) and (-2,3) and whose semi - minor axis is sqrt(5) .

The length of minor axis of the ellipse 9x^(2) + 4y ^(2) = 36 is _

Consider the ellipse E_1, x^2/a^2+y^2/b^2=1,(a>b) . An ellipse E_2 passes through the extremities of the major axis of E_1 and has its foci at the ends of its minor axis.Consider the following property:Sum of focal distances of any point on an ellipse is equal to its major axis. Equation of E_2 is

The length of the semi-major axis of an ellipse is 13 and its eccentricity is 12/13. Then the length of the semi-minor axis is

The distance between the vertices of a hyperbola is half the distance between its foci and the length of its semi-conjugate axis is 6. Referred to its axes of coordinates, find the equation of the hyperbola.

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.

A square of side a lies above the x-axis and has one vertex at the origin. The side passing throuhg the origin makes an angle alpha (0 lt alpha lt (pi)/(4)) with the positive direction of x-axis. Then the equation of its diagonal not passing through the origin is-

The length of latus rectum of an ellipse is equal to the length of its semi-minor axis . The ratio of lengths of its minor axis and major axis is _