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

Show that the equaion x ^(2) + y ^(2) - 6x + 4y - 36 = 0 represents a circle. Also, find its centre and radius.

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

If the equation (4 lambda - 3) x^(2) + lambda y ^(2) + 6x - 2y + 2 = 0 represents a circle, then its centre is

Show that the equation 5x^(2) + 9y ^(2) - 10 x + 90 y + 185 = 0 represents an ellipse and find the equations of the directrices of this ellipse .

Show that the equation 9x^(2) - 16y^(2) - 18x - 64y - 199 = 0 represents the equation of a hyperbola, find the coordinates of its centre and foci and also the equations of its directrices

If the equation kx^(2) + (2k - 3) y^(2) - 6x + 4y + 3 = 0 represents a circle, then its centre is

If x^2 + y^2 - 6x + 4y - 12 = 0 represents a circle, then find its parametric equations.

Prove that the equation x^2 + y^2 + 2gx + 2fy + c = 0 represents a circle and find its centre and radius.

Find the value of aif 2x^(2) + ay^(2) -3x + 2y -1 =0 represents a circle and also find its radius