>>14405686First, you're the dumb shit asking basic shit so you have no right to call insult anybody by calling them "troll", "retard", or "faggotron". You could've used /sqt/, but you didn't.
Second,
>equation of an ellipseAn equation alone tells you nothing about the shape it takes when plotted. You only interpret that equation as an ellipse because you plot it against xy-axis, which means you interpret (x, y) as variables while you interpret (h, k, a, b) as parameters. But if you plotted it against ab-axis you would get this shape
>>14405734. Which, of course, you called retarded because you're a dumb shit.
If you want to determine the shape an equation such as
You first have to decide which parts you're going to interpret as variables and which paramaters. You set the parameters to a constant value while you allow variables to take all possible values for which the equation holds true and you get a certain shape. The parameters you set define how that shape will look like, while the variable solutions are the specific points on that shape. For example, if you consider (x, y) variables you get an ellipse, and you can control the width and center of that ellipse using parameters (h, k, a, b). On the other hand, if you consider (a, b) as variables you get this shape
>>14405734, and you can similarly control how that shape looks like with specific values for parameters (x, y, h, k).
Any element of the equation can be a parameter or a variable.
You could consider all six to be variables, in which case they define a shape in 6-deminsional space.
And you could also consider only e.g. to be a variable, in which case the shape reduces to a quadratic curve.
Whether something is a variable or a parameter in an equation is entirely up to interpretation but (x, y, z) usually denote variables while (a, b, c) usually denote parameters.
