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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.
How does ellipse differ from a circle?
ellipse is the shape of an egg
Is an oval a graph of a function?
No, the graph of an oval/ellipse is not a function because it does not pass the vertical line test.
What happens to the graph of an ellipse when y is replaced by y plus 6?
The whole ellipse shifts down by 6 units.
How can you tell if the graph of an equation in the form ax2 plus by2 equals c is a circle or an ellipse?
If a = b then it is a circle; otherwise it is an ellipse.
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.
Is the graph of an ellipse a function?
Yes. It's the graph of [ Y = f(X) ] described by (X/A)2 + (Y/B)2 = C2 A, B, and C are constants. If 'A' and 'B' are both '1', then the graph is a circle with radius 'C'.
Which equation below represents a generic equation suggested by a graph showing a hyperbola?
A hyperbola is another form of a conical section graph like a parabola or ellipse. Its general form is x^2/a - y^2/b = 1.
Is an ellipse a function?
No. A function is a "graph" the survives the "vertical line test". Namely, it is for every x in its domain, there can be one and only one f(x) in its co-domain. An ellipse clearly fails it at everywhere except it's two vertex. But an ellipse can be thought as two separate functions. A standard ellipse relation, x^2 / a + (y)^2 / b = 1, can be thought as two separate real functions of y1 and y2. where y1 = -y2 exactly.
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 of an ellipse can be outside the ellipse?
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
Can the foci of an ellipse be outside of the ellipse?
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
CanThe foci of an ellipse can be outside the ellipse?
No. Both foci are always inside the ellipse, otherwise you don't have an ellipse.
