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

The equation 16x^2+y^2+8xy-74x-78y+212=0 represents:

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

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

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

The equation x^(2)+3y^(2)-9x+2y+1=0 represents

If px^2-10xy + 12y^2+ 5x - 16y - 3 = 0 represents a pair of straight lines, then value of p is :

The differential equation (dx)/(dy)=(3y)/(2x) represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity.

Find all the aspects of hyperbola 16x^(2)-3y^(2)-32x+12y-44=0.

The system of equations x+2y=3,2x-3y=5 and x -12y =1 has