Show that `3x^2 + 4y^2 - 12x - 8y + 4 = 0` represents an ellipse. Find its centre, lengths and equations of axes, eccentricity, foci and directrices.

Show that the equation : 16x^2 -3y^2-32x -12y- 44 = 0 represents a hyperbola , and find the lengths of the axes and eccentricity.

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

Show that 4x^2+8x+y^2-4y+4=0 represents an ellipse. Find its eccentricity, co-ordinates of foci, equations of major and minor axes and latus-rectum.

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

Show that the equation 7x^(2)-9y^(2)+54x-28y-116=0 represent a hyperbola. Find the coordinate of the centre, lenghts of transverse and conjugate axes, eccentricity, latusrectum, coordinates of foci and vertices of the hyperbola.

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

The equation (x^(2))/(10-a)+(y^(2))/(4-a)=1 represents an ellipse , if

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

The equation ax^2+4xy+y^2+ax+3y+2=0 represents a parabola. Find the value of a .

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