Show that the following equations represent ellipses. Find their foci, vertices, eccentricity and directrices :
`4x^2 + 16y^2 - 24x - 32 y - 12 = 0`.

Find the centre, eccentricity, foci and directrices of the hyperbola : 9x^2-16y^2+ 18x +32y-151 = 0 .

Find the centre, eccentricity, foci and directrices of the hyperbola : x^2-3y^2-2x=8.

Show that : 4x^2+16y^2-24x-32y=12 is the equation of ellipse, and find its vertices, foci, eccentricity and directrices.

Find the centre, length of the axes, eccentricity and foci of the ellipse : 12x^2+4y^2+ 24x -16y+25=0 .

Find the lengths of the major and minor axes, co-ordinates of the foci, vertices, the eccentricity and equations of the directrices for the ellipse 9x^2+ 16y^2 = 144 .

The eccentricity of the ellipse 4x^2 + 9y^2 = 36 is :

The eccentricity of the ellipse : x^2+4y^2+8y-2x+1=0 is :

Show that the equation (10x-5)^(2)+(10y-5)^(2)=(3x+4y-1)^(2) represents an ellipse, find the eccentricity of the ellipse.

Factorise : 4x^2+9y^2+16z^2+12xy-24yz-16xz .

In the following, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. 9y^2 - 4x^2 = 36