### 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**

**x=r*cos θ**

**θ=tan-1(y/x)**

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.Limaςon

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) -> ellipseabs(a)

*is less than*abs(b) -> hyperbolaNote: 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!

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