Focus of a Parabola (vertex at h,k)

Focus of a Parabola (vertex at h,k)

by JadeAnthony Dosdos

​Today's agenda:

Objectives:

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​Explore the focus and directrix of a parabola.

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​Write the equations of a parabola at a given vertex of (h,k).

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Steps on how to solve given the vertex and the focus:

​1. Determine what coordinates that has been changed.

​2. Once determined, choose the equation that corresponds to the changes.

​3. Solve for p and look for the focus part/formula.

​4. Substitute the value of p and the value of vertex in the given equation.

​Example:

​1. Write an equation of a parabola with vertex (-1,4) and focus (-1,2).

​Solution:

​4+p = 2

​p = 2-4

​p = -2

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​y = 1/4p (x-h)²+k

​y = 1/4(-2) (x-(-1))²+4

​y = -1/8 (x+1)²+4

Multiple Choice

Write an equation of a parabola with a vertex of (-4, -1) and focus of (-4,6).

• $$y=\frac{1}{28}\left(x+4\right)^2-1$$  

• $$y=-\frac{1}{28}\left(x+4\right)^2+1$$  

• $$y=\frac{1}{20}\left(x-4\right)^2-1$$  

• $$y=-\frac{1}{20}\left(x-4\right)^2-1$$  

​Steps on how to solve given the vertex and the directrix:

​1. Determine what letter has been given.

​2. Once determined, choose the equation that corresponds to the letter.

​3. Solve for p and look for the directrix part/formula.

​4. Substitute the value of p and the value of vertex in the given equation.

​Example:

​Write an equation of a parabola with vertex (2, -4) and directrix of y = -6.

​Solution:

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​                     -6 = -4 - p

​                   -6 + 4 = - p

​                          -2 = -p

​                             2 = p

Multiple Choice

Write an equation of a parabola with vertex (-4, -1) and directrix of y = -8.

• $$x=-\frac{1}{28}\left(y+4\right)^2-1$$  

• $$y=-\frac{1}{28}\left(x+4\right)^2-1$$  

• $$x=\frac{1}{28}\left(y+4\right)^2-1$$  

• $$y=\frac{1}{28}\left(x+4\right)^2-1$$  

Poll

Do you have any questions?

• Yes

• No