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Unit 4 - Coggle Diagram

- - - - Coordinate: how to find a point in a space
      - Rectangular coordinates (直角坐标) (x, y)
      - Polar coordinates (r, θ)
      - Rectangular to Polar:
        
        Given y=f(x), find r=g(θ)
        
        Substitute y=r sin⁡θ, x=r cos⁡θ
        
        Given r=g(θ), find y=f(x)
        
        Substitute r=√(x^2+y^2 ),tan⁡〖θ=y/x, sin θ=y/r,cos⁡〖θ=x/r, … 〗〗
    - - Conics (圆锥曲线) general equation
        
        Ax^2+Bxy+Cy^2+Dx+Ey+F=0
      - Parabolas: Either A=0, or C=0, not both
        
        Regular and sideway, vertex (h, k)
        
        y=a(x−h^2+k
        
        x=a(y−k)^2+h
      - Rectangular Hyperbolas: AC=−1
        
        Horizontal: (x−h^2/a^2 −(y−k)^2/b^2 =1
        
        Vertical: (y−k)^2/a^2 −(x−h^2/b^2 =1
        
        What is a and b on a graph?
    - - Circles: A=C
        
        (x−h^2+(y−k)^2=r^2, or (x−h^2/r^2 +(y−k)^2/r^2 =1
      - Ellipses: AC>0, A≠C
        
        Horizontal Ellipse a>b: (x−h^2/a^2 +(y−k)^2/b^2 =1
        
        Vertical Ellipse a>b: (y−k)^2/a^2 +(x−h^2/b^2 =1
        
        Major axis and Minor axis