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.

​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

​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

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