All right, so Conics is one crazy unit. Started out learning about the ancient Japanese art from Samurai Kuro Pat Wa and all the different shapes you can form from cutting a cone. A cone is basically if you took a line and just spun it around. From here you can cut out 4 shapes. You can cut out a circle, an ellipse, a parabola, and a hyperbola. Each one is different.
Some commonalities include:
- Vertices
- Foci
- Focal Radii
- Locuses (Loci?) of points
Equations to remember~
Parabola:
- (x-h)^2=4p(y-k) (vertical parabola)
- (y-k)^2=4p(x-h) (horizontal parabola)
- (h,k)=Vertex
- p=distance from vertex to directrix or a focal point
Circle:
- (x-h)^2+(y-k)^2=r^2
- r=radius
- (h,k)=center
Ellipse:
- ((x-h)^2/a^2)+ ((y-k)^2/b^2)=1 *horizontal*
- ((y-k)^2/a^2]+[(x-h)^2/b^2)=1 *vertical*
- a=semimajor axis
- b=semiminor axis
- c= distance from center to foci
- (h,k)=center
Hyperbola:
- ((x-h)^2/a^2)-((y-k)^2/b^2)=1 *horizontal*
- ((y-k)^2/a^2)-((x-h)^2/b^2)=1 *vertical*
- a= transverse axis
- b= conjugate axis
- c= distance to foci
- (h,k)=center
My struggles:
- Have had some trouble in identifying vertical/horizontal in some instances.
- Sometimes get confused between the ellipse and hyperbolic equations.
- Issues with completing the square.
But I have done some looking over things this weekend and, all in all, this un it is not extremely difficult and so hopefully I will do quite well on it. Next period here I come!
~ Pokemon Champion
