10 2 Parabolas Parabola Set of all points

10 – 2 Parabolas

Parabola • Set of all points in a plane that are the same distance from a fixed line and fixed point on on the line • Focus: fixed point • Directrix: fixed line • Focal length: distance between the vertex and the focus

Vertical Parabolas • • • Finding the equation with the vertex at the origin Form y = ax 2 Focus (0, c) Directrix: y = -c Coefficient: a = 1/4 c • (this is how you find the focus and directrix )

Write the Equation • What is the equation of the parabola with vertex at the origin and focus (0, 2)? • What is the focus and directrix of the parabola with equation y = -(1/12)x 2 • What is the equation of the parabola with vertex at the origin and focus (0, -1. 5)? • What is the focus and directrix of the parabola with equation y = x 2/4 • How does the distance from the focus affect the shape of the parabola?

Horizontal Parabolas • • • Finding the equation with the vertex at the origin Form x = ay 2 Focus (0, c) Directrix: y = -c Coefficient: a = 1/4 c • (this is how you find the focus and directrix )

Write the Equation • What is the equation of a parabola with vertex a the origin and directrix x = 1. 25? • What are the vertex, focus, and directrix of the parabola with equation x =. 75 y 2? • What is the equation of a parabola with vertex a the origin and directrix x = -5/2? • What are the vertex, focus, and directrix of the parabola with equation x = -4 y 2?

Real World Application • The focus has a very important reflective property • This allows satellites to work

• The mirrored reflector of a flashlight is 8 cm across and 4 cm deep. How far from the vertex should the light bulb be positioned?

Transformations

• What are the vertex, focus, and directrix of the parabola with equation y = x 2 +8 x +18? • hat are the vertex, focus, and directrix of the parabola with equation y = x 2 -6 x +15?

• What is the equation of the parabola with vertex(1, 4) and focus(1, 6)

Homework • Pg. 627 • #8 – 38 even, 40