Section 13.2: polar equations of conics and other curves
POLAR EQUATIONS OF CONICS AND OTHER CURVES
This section gives you the basic information about polar equations and how to relate polar coordinates (r,θ) with cartesian coordinates (x,y).
Polar coordinates are a different way of identifying a point in space. With polar coordinates we use a radius (r) and an angle (θ) to specify a point. The coordinate plane looks like this:
To relate r, θ, x, and y, we can use the following trigonometric equations.
x^2 + y^2 = r^2
sin θ = y/r
sin θ = y/r
From these equations we can derive values for x,y, and θ.
y= r*sin θ
Now, we need to know how to plot polar graphs on our calculators. First, we need to change the mode to polar. When you go to the y= menu it will now say r=. The standard equation for a polar graph is r=a+bsinθ or r=a+bcosθ. These equations will result in a limaςon or cardioid.
The last bit of information in this section is the general polar equations for conic sections.
These equations are r= k / (a+bsinθ) or r = k / (a+bcosθ). With these equations you can make a parabola, ellipse, or hyperbola.
Depending on the relationship of a and b you will get a different conic shape.
abs(a) = abs(b) -> parabola
abs(a) is greather than abs(b) -> ellipse
abs(a) is less than abs(b) -> hyperbola
Note: the focii of a parabola will be at the origin as well as one of the focii of a ellipse or hyperbola.
Thats it for now!
for more info check out http://en.wikipedia.org/wiki/Polar_coordinate_system
Next up is EDWARD
IF YOU DONT KNOW POLAR EQUATIONS THIS WILL HAPPEN TO YOU!