Focus of a Parabola

Focus of a Parabola

* Explore the FOCUS and DIRECTRIX of a parabola.

*Write equations of a parabola.

Parabola

- can be defined as the set of all points (x,y) in a plane that are equidistant from a fixed point called the FOCUS and the fixed line is DIRECTRIX.

Multiple Choice

The focus is always inside the parabola.

• True

• False

Multiple Choice

The vertex is halfway between the focus and directrix.

• True

• False

​Example:

• ​Identify the focus and directrix of -4x=y².

​

​Solution:

​-4x = y² (divide both sides by -4)

​ x = y²/-4

​

​4p = -4 (divide both sides by 4)

​ p = -1

​

​Focus: (p,0) ( -1 , 0 )

​Directrix: x = -p

​ x = - (-1)

​ x = 1

Multiple Choice

Identify the focus and directrix of -2x = y².

• focus is (0.5, 0)

  directrix is x = -0.5

• focus is (-0.5, 0)

  directrix is x = 0.5

• focus is (0, -0.5)

  directrix is x = -0.5

• focus is (0, -0.5)

  directrix is x = 0.5

​Example:

​Write an equation of the parabola with the vertex at (0,0) and the given directrix or focus.

​1. directrix: x = -3

​2. focus: (-2,0)

​Solution:

​1. Directrix: x = -3

​Since, x = -p

​ p = -(-3)

​ p = 3

​Then, x = 1/4p y²

​ x = 1/4(3) y²

​ x = 1/12 y²

​Solution:

​2. Focus: (-2,0)

​Since, (p,0)

​ p = -2

​Thus, x = 1/4p y²

​ x = 1/4(-2) y²

​ x = 1/-8 y² or

​ x = -1/8 y²

Multiple Choice

What is the equation of the parabola if the directrix is x = 4?

• y = 1/16x²

• x = 1/16y²

• y = -1/16x²

• x = -1/16y²

Multiple Choice

What is the equation of the parabola if the focus is (0,3)?

• y = -1/3x²

• y = 1/12x²

• y = 1/3x²

• y = -1/12x²

Open Ended

Do you have any questions?

​Go to GOOGLE CLASSROOM and answer the "Guided and Independent Practice".