An ellipse and a hyperbola have their principal axes along the coordinate axes and have common foci separated by a distance `2sqrt3`. The difference of their focal semi-aixes is equal to 4. It the ratio of their accentricities is `3//7`, find the equaiton of these curves.

An ellipse and a hyperbola have their principal axes along the coordinate axes and have a common foci separated by distance 2sqrt(3)dot The difference of their focal semi-axes is equal to 4. If the ratio of their eccentricities is 3/7 , find the equation of these curves.

Find the equation of hyperbola : whose axes are coordinate axes and the distances of one of its vertices from the foci are 3 and 1

Find the perpendicular distances of the point (2,3,4) from the coordinates axes

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is

Find the equation of a hyperbola whose eccentricity is 5/4 and the. coordinate of foci are (2, -3)and (2, 5).

Find the coordinates of the points on y - axis which are at a distance sqrt(41) unit from the point ( 3 , 2 , -4) .

Two gases, A and B having equal mass are kept in two separate vessels under identical conditions of temperature and pressure. If the ratio of their molecular masses be 2:3, find the ratio of the volumes of the vessels.

An ellipse intersects the hyperbola 2x^2-2y^2 =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (+-sqrt 2, 0) (d) equation of ellipse is (x^2 +y^2 =4)

Find the perpendicular distances of the point ( 2 ,3 , 4) from the z coordinate axes .

Find the equation of the hyperbola, whose axes are axes of coordinates and eccentricity is sqrt((3)/(2)) and the length of semi-latus rectum is 2.