Summary
With the help of this activity, we have learnt that:
When a=b and h=0 then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be a circle and vice versa.
When h^2=ab then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be a parabola and vice versa.
When h^2<ab then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will be an ellipse and vice versa.
When h^2>ab then the conic ax^2+2hxy+by^2+2gx+2fy+c=0 will be a hyperbola and vice versa.
When abc + 2fgh – af2 – bg2 – ch2 = 0 then the conic section ax^2+2hxy+by^2+2gx+2fy+c=0 will become a pair of straight lines and vice versa.
