General equation of second degree of the form ax^2+2hxy+by^2+2gx+2fy+c=o

Steps involved in solving this please, with an example.

In a second degree general equation, first the discriminant and determinant need to be examined.

if ? ≡ abc + 2fgh − af2 − bg2 − ch2 = 0 then the equation represents a pair of straight lines.

If not zero, then we examine the discriminant(D): (2h)^2-4ab = 4(h^2-ab)

• If the D=0, then it represents a parabola.
• if D<0 and h≠0 and a≠b, then it is an ellipse.
• if D<0 and h=0 and a=b, then it is a circle.
• if D>0 then it is a hyperbola. if a+b=0, then it is a rectangular hyperbola.

After analysing this, we proceed to the solutions accordingly.