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As you may or may not be aware, there are multiple co-ordinate systems by which a graph may be defined. An ellipse graph has the general equation in the following systems:
Cartesian (what most people are used to): (X-H)^2 (Y-K)^2
---------- + ----------- = 1 (A,B,H,K are constants) A^2 B^2
Polar: r(θ)= sqrt( (bcos(θ))^2+(asin(θ))^2 )
Parametric: x = a cos(t) , y = b sin(t)
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What does a nonlinear graph look like?
any graph that is not represented by a line,ie: parabola, hyperbola, circle, ellipse,etc
Is a graph of a quadratic function always a parabola?
No. It can also be a circle, ellipse or hyperbola.
How can you tell when you are going to graph and Ellipse?
ax^2+by^2=k is an ellipse this is not in standard form which is x^2/a^2+y^2/b^2=1 but you will often see ellipses written this way. ellipses are also commonly written in their parametric form which is x=ccos(t) and y=dsin(t). finally a circle is a special case of an ellipse and if a b or k are 0 or negative it is not an ellipse. c and d can be positive but not 0.
Can the foci's of and ellipse be outside the ellipse?
No.
Is the focus of an ellipse always inside the ellipse?
Yes, they are.
