Focus of a Parabola (vertex at h,k)
Presentation
•
Mathematics
•
9th - 12th Grade
•
Medium
JadeAnthony Dosdos
Used 16+ times
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7 Slides • 3 Questions
1
Focus of a Parabola (vertex at h,k)
by JadeAnthony Dosdos
2
Today's agenda:
Objectives:
Explore the focus and directrix of a parabola.
Write the equations of a parabola at a given vertex of (h,k).
3
4
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.
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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
y = 1/4p (x-h)2+k
y = 1/4(-2) (x-(-1))2+4
y = -1/8 (x+1)2+4
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Multiple Choice
Write an equation of a parabola with a vertex of (-4, -1) and focus of (-4,6).
y=281(x+4)2−1
y=−281(x+4)2+1
y=201(x−4)2−1
y=−201(x−4)2−1
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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.
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Example:
Write an equation of a parabola with vertex (2, -4) and directrix of y = -6.
Solution:
-6 = -4 - p
-6 + 4 = - p
-2 = -p
2 = p
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Multiple Choice
Write an equation of a parabola with vertex (-4, -1) and directrix of y = -8.
x=−281(y+4)2−1
y=−281(x+4)2−1
x=281(y+4)2−1
y=281(x+4)2−1
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