For the ellipse `4x^(2)+y^(2)+24x-2y+21=0`, find the centre, vertices, and the foci. Also prove that the length of latus rectum is 2.

For the ellipse 4x^(2)+3y^(2)+8x+12y+4=0 . Find the centre, vertices, foci and latus rectum.

Find the coordinates of the vertices and the foci and the length of the latus rectum of the ellipse 9x^(2)+25y^(2)=225 .

For the hyperbola, 3y^(2) - x^(2) = 3 . Find the co-ordinates of the foci and vertices, eccentricity and length of the latus rectum.

For the hyperbola, 3y^(2) - x^(2) = 3 . Find the co-ordinates of the foci and vertices, eccentricity and length of the latus rectum.

Find the eccentricity, the coordinates of the foci, and the length of the latus rectum of the ellipse 2x^(2)+3y^(2)=1 .

Find the lengths of the major and minor axes, coordinates of the vertices and the foci, the eccentricity and length of the latus rectum of the ellipse: 4x^(2)+9y^(2)=144.

Find the lengths of the major and minor axes, coordinates of the vertices and the foci, the eccentricity and length of the latus rectum of the ellipse: 4x^(2)+y^(2)=100.

Find the lengths of the major and minor axes, coordinates of the vertices and the foci, the eccentricity and length of the latus rectum of the ellipse: x^(2)/4+y^(2)/36 = 1.

Find the foci, vertices, the eccentricity and the length of the latus rectum of the hyperbola 16x^2-9y^2=144 .

Show that x^2+4y^2-2x+16 y+13=0 is the equation of an ellipse. Find its eccentricity, vertices, foci, directices and , the length and the equation of the latus-rectum.