Show that the following equations represent ellipses. Find their foci, vertices, eccentricity and directrices :
`x^2 + 4y^2 - 2x = 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, eccentricity, foci and directrices of the hyperbola : 9x^2-16y^2+ 18x +32y-151 = 0 .

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

Show that the equation y^2 - 8y -x+19 = 0 represents a parabola. Find its vertex, focus and directrix.

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 .

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

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

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

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