Algebra II

Section 8-2

Parabolas

(the dreaded lesson)

Conic Sections

Find a point equidistant from (2, 3) and the line y = -1

Distance from (x, y) to (2, 3) = Distance from (x, y) to (x, -1)

22 )3()2( yx 22 )1()( yxx222 )1()3()2( yyx

1296)2( 222 yyyyx

88)2( 2 yx

8)2(8 2 xy

1)2(8

1 2 xyThis is a parabola!

Properties of ParabolasAll incoming parallel rays are reflected to the same point (focus).

This is true for light, sound, radio, …

a4

1

a4

1

khxay 2)(

Vertex = (h, k)

)4

1,(

akh

Focus

Line segmentthrough the focusParallel to the directrix

a

1Length

Name : Latus Rectum .

aky

Directrix

4

1

Sideways?

• See chart on page 422

Mythbusters

Illusion

Parabola A

Parabola BFocus of A

Focus of B

Find the Focus, Vertex, Directrix, Axis of Sym., Length of the L.R.

• y = -2x2– 20x + 9Put in Vertex Form

y = -2(x + 5)2 + 59

Focus = (-5, 58.875)

Vertex = (-5, 59)

Directrix y = 59.125

Length of L.R. = 0.5

Axis of Sym. x = -5

• Page 423 # 1-41 odd