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Conics: Circle

Conics: Circle. By: Jay, Tyler, Bailey, Grace, Ryan, and Jesse. Origin of a Circle. A circle is formed when a plane is put through a cone and it is perpendicular to the axis of the cone and intersects each generator. To construct a circle you need a fixed point (center), and a radius.

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Conics: Circle

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  1. Conics: Circle By: Jay, Tyler, Bailey, Grace, Ryan, and Jesse

  2. Origin of a Circle • A circle is formed when a plane is put through a cone and it is perpendicular to the axis of the cone and intersects each generator. • To construct a circle you need a fixed point (center), and a radius

  3. Forms of a Circle • Algebra II form: (x-a)² + (y-b)² = r² • Conic Form: Ax²+Cy²+Dx+Ey+F=0 if A=C • Rotated Form: Ax²+Bxy+Cy²+Dx+Ey+F=0 if B²-4AC<0 Standard Form: x²+y²=r² (at origin) (x-h)²+(y-k)²=r² (not at origin) Relationships – Center (a,b) or (h,k), radius= r Radius- Half the width, Diameter- The width

  4. Circle info • Degenerate Case – A circle with a radius of zero is a point, radius approaches 0, until it becomes a point. • Application – Changing the radius or origin to move the circle. • Eccentricity- The eccentricity of a circle is zero. Eccentricity is how much the conic deviates from being circular.

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