Show that the equation ` x ^(2) + y ^(2) - 3x + 3y + 10 = 0 ` does not represent a circle.

Prove that the equation 3x^(2) + 3y^(2) - 5x + 6y + 8 = 0 does not represent circle.

Show that the equation x ^(2) + y ^(2) + 2x + 10 y + 26 = 0 represents a point circle. Also, find its centre.

Show that the equation 2x^(2) + xy - y^(2) + x + 4y - 3 = 0 represents a pair of lines.

If the equation 3x^(2) + 3y^(2) + kxy + 9x + (k - 6) y + 3 = 0 represents a circle , then the radius of this circle is

If the equation a^(2) x^(2) + (a^(2) - 5a + 4) xy + (3a - 2) y^(2) - 8x + 12y - 4 = 0 represents a circle , then : a =

Show that the equation 3x^(2)+3y^(2)+6x-4y-1=0 represents a circle Find its centre and radius.

Show that the equation 3x^(2)+3y^(2)+12x-18y-11=0 represent a circle.Also find its centre and radius.

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