U5 Conic Sections(KA/PRE/U5)

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Unit 5: Conic Sections

Introduction to Conic Sections

Conic sections include circles, ellipses, parabolas, and hyperbolas, formed by slicing a cone at various angles.

Center and Radii of an Ellipse

The standard form of an ellipse: (x - h)²/a² + (y - k)²/b² = 1. Center at (h, k), radii a and b.

Foci of an Ellipse

The distance to each focus is c = √(a² - b²), located along the major axis from the center.

Introduction to Hyperbolas

Standard form: (x - h)²/a² - (y - k)²/b² = 1 (horizontal), or flipped for vertical hyperbola.

Foci of a Hyperbola

Distance to each focus is c = √(a² + b²), further from the center than the vertices.

Hyperbolas Not Centered at the Origin

The center (h, k) shifts the hyperbola horizontally or vertically on the plane.

Quiz: Test Your Understanding

What type of conic section has two foci inside the curve?

  1. Circle
  2. Ellipse
  3. Hyperbola

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