If `C` is the center of the ellipse `9x^2+16 y^2=144` and `S` is a focus, then find the ratio of `C S` to the semi-major axis.

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

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

Calculate the eccentricity of the ellipse (x^(2))/(169)+(y^(2))/(144) = 1

An ellipse is drawn by taking a diameter of the circle (x-1)^(2) + y^(2) = 1 as its semi-minor axis and a diameter of the the circle x^(2) +(y - 2)^(2) = 4 as its sem-major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes , then the equation of the ellipse is _

Find the equation of the tangent to the ellise x^(2)+16y^(2)=16 at the point (4 cos alpha, sin alpha) . Hence , find the equation of the tangnets to the ellipse which are inclined at an angle 60^(@) to x-axis.

If the coordinates of a point lies on the ellipse 9x^2+16y^2=144 be (2,(3sqrt3)/2) ,find the eccentric angle of that point.

The eccentricity of an ellipse is (4)/(5) and the coordinates of its one focus and the corresponding vertex are (8,2) and (9,2) . Find the equation of the ellipse. Also find in the same direction the coordinates of the point of intersection of its major axis and the directrix.

P is the point on the ellipse is x^2/16+y^2/9=1 and Q is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

The coordinates of the centre of the ellipse 4x^(2) + 9y^(2) - 16 x + 18 y - 11 = 0 are _

Find the vertices of the hyperbola 9x^2-16 y^2-36 x+96 y-252=0