Write down the conditions which should be satisfied by the constants a,g, f and c so that `a(x^2 + y^2) + 2 gx + 2fy + c = 0` may represent a circle.

The general equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a circle if

The general equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a circle if:

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

Find (dy)/(dx) in the following : ax^2 + 2hxy + by^2 + 2gx + 2 + y + c = 0

The eccentricity of ellipse ax^2 + by^2 + 2gx + 2fy + c = 0 if its axis is parallel to x-axis is

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

Find the area of the region which is inside the parabola satisfying the condition |x-2 y|+|x+2y|le 8 and xy ge 2 .

The common tangents to the circles x^2 + y^2 + 2x =0 and x^2 + y^2-6x=0 form a triangle which is

If two curves whose equations are ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 and a'x^2 + 2h'xy + b'y^2 + 2g' x + 2f' y + c = 0 intersect in four concyclic point., then prove that a-b/h = a-b/h

Find the condition for the curves (X^2)/(a^2) - (y^2)/(b^2) = 1 and xy = c^2 to intersect orthogonally.