Conic Sections
Conic sections are special graphs. Their shapes can actually be derived from a cone. They are different from most other graphs that we discuss here as the y-variable in their equations are usually in second degree.
As you will soon notice, the general equations for each conic section involve the variables in x2 and y2 form. Hence, if you see x2 and y2 in an equation, to sketch its graph, simply complete the square and see which of the following categories it falls under.
Circle
The general equation of a circle is
(x - a)2 + (y - b)2 = r2
where the centre is at (a,b) and radius r.
Graph of x2 + y2 = 1
Ellipse
The general equation of an ellipse is
where (a,b) is the centre, c is the major axis (the distance from centre to graph along the horizontal) and d is the minor axis (the distance from centre to graph along the vertical).
As you can see, the ellipse is very similar to the circle. Actually, the circle is a special case of the ellipse, when c = d = 1.
Graph of
Hyperbola
There are two types of hyperbolas with slightly different general equations.
where x = |c| are the intercepts and
y = |d/c|x are the asymptotes.
Graph of x2 - y2 = 1
where y = |d| are the intercepts and
y = |d/c|x are the asymptotes.
Graph of y2 - x2 = 1
Curve Sketching | Quadratic Equation | Rectangular Hyperbolas | Conic sections | Modulus Functions
