My polar equation pic

Polar coordinates.

This week we learned about pole cordintes.  Those are points on a circular graph.  It contains a r and a angle value. When graphing, if the angle is positive, we look counterclockwise, and if the angle is negative, we count clockwise. We could switch polar and rectangular coordinates back and force. From polar to rectangular, we use x=rCosø and y=rsinø to get x and y value 

Parabola

This week we talked about prabola. Prabola is a u shape graph either going up and down or left or right. Parabolas have derixtrice.  It also has a focus.  The directrix for vertical graphs is y=k-c and for horizontal graph is x=h-c.  The prabola is symmetric, and there is a axis of symmetry.  The equation for parabola is (x-h)^2=4c(y-k).  If the graph is side to side, the equation's x and y switches.  The focus is (h, k+c) and vertices is (h,k).   

rotating conic

When we graph a conic graph that is tilted, we could try to rewrite it back into the normal equation.  The equations have angles, to rewrite this equations, we first need to find the angle.  Cot2x=A-C/B.    We get the A,B,C values from the equation given.  Ax^2+Bxy+Cy^2+Dx+ey+F=0. He second step is to replace x and y with x'cosø-y'sinø and x!sinø+y'cosø.  The last step is to plug in the x and y into the equation. After plugging in, we just do algebra and simplify the new equation.   And now we have a new equation for the rotated conic graph.