x^2+2hxy+by^2+2gx+2fy+c=0, depends upon a, b,c,h,g,f
General equation of a conic section is ax^2+2hxy+by^2+2gx+2fy+c=0 and its shape depends upon the different values of a, h, b, g, f and c. We can change the values of a, h, b, g, f and c using their respective slide bars and observe how the shape of the conic section changes. We can see an equation and graph of a conic section in blue color. By seeing the equation we can figure out what the values of a, h, b, g, f and c are for this particular conic section graph.
Question/s to think about. Make a=b and h=0, what do we observe? Make〖 h〗^2=ab, what do we observe? Make h^2<ab, what do we observe? Make〖 h〗^2>ab, what do we observe? Make abc + 2fgh – af2 – bg2 – ch2 = 0, what do we observe? Hint, make a=-5, b=1, c=1, f=1, g=1 and h=1