Grade 11 · Math · Algebra 2

11th grade Parabolas: focus, directrix and equations worksheet

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Parabolas: focus, directrix and equations

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

1.
Luz designs a lamp reflector with its focus at (2, 5) and its directrix y = 1. Which equation is the reflector's curve?
- (x − 2)² = 8(y − 3)
- (x − 2)² = 16(y − 3)
- (y − 3)² = 8(x − 2)
- (x + 2)² = 8(y + 3)
2.
Milo marks the focus (5, -1) and the directrix x = 1 on graph paper. Which equation is the parabola?
- (y + 1)² = 16(x − 3)
- (y + 1)² = 8(x − 3)
- (y − 1)² = 8(x + 3)
- (x − 3)² = 8(y + 1)
3.
Noah plans a fountain's arc of water with focus (-1, -4) and directrix y = 2. Which equation is the arc?
- (x − 1)² = -12(y − 1)
- (x + 1)² = -12(y + 1)
- (y + 1)² = -12(x + 1)
- (x + 1)² = -24(y + 1)
4.
Ren marks the focus (-6, 2) and the directrix x = 2 on graph paper. Which equation is the parabola?
- (y − 2)² = -32(x + 2)
- (y − 2)² = -16(x + 2)
- (y + 2)² = -16(x − 2)
- (x + 2)² = -16(y − 2)
5.
Tala writes a parabola on graph paper as x² − 8x − 8y + 8 = 0. Which equation is the same curve in standard form?
- (x − 4)² = 8(y + 3)
- (x − 4)² = 8(y + 1)
- (x − 4)² = 8(y − 1)
- (x + 4)² = 8(y + 1)
6.
Zee writes a lamp reflector's curve as y² + 12y − 12x + 48 = 0. Which equation is the same curve in standard form?
- (y + 6)² = 12(x − 1)
- (y + 6)² = 12(x − 4)
- (y + 6)² = 12(x + 7)
- (y − 6)² = 12(x − 1)
7.
Esme writes a fountain's arc of water as x² + 4x + 4y − 8 = 0. Which equation is the same curve in standard form?
- (x + 2)² = -4(y − 2)
- (x + 2)² = -4(y + 1)
- (x − 2)² = -4(y − 3)
- (x + 2)² = -4(y − 3)
8.
Jun writes a parabola on graph paper as y² − 8y + 8x + 24 = 0. Which equation is the same curve in standard form?
- (y − 4)² = -8(x + 1)
- (y − 4)² = -8(x − 5)
- (y + 4)² = -8(x + 1)
- (y − 4)² = -8(x + 3)
Luz writes a parabola on graph paper as y = (1/12)(x − 2)² + 3. Where is its focus?
Ren writes a parabola on graph paper as y = (1/4)(x + 5)² + 1. Where is its focus?

11th grade Parabolas: focus, directrix and equations worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Parabolas: focus, directrix and equations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the focus, directrix and axis of a parabola from its equation, using 4p.
I can write a parabola's equation from its focus and directrix: the vertex is halfway, and p is half the gap.
I can complete the square to turn x² − 8x − 8y + 8 = 0 into (x − 4)² = 8(y + 1).

Standard: G-GPE.A.2

Words to know

parabola: Every point as far from one marked point as from one line.

focus: The marked point inside the curve.

directrix: The marked line outside the curve.

vertex: The turning point, halfway between the focus and the directrix.

p: The distance from the vertex to the focus; the equation shows 4p.

axis of symmetry: The mirror line through the vertex and the focus.

Common mistakes

Your child used the whole number in the equation as the distance to the focus, instead of a quarter of it.

Your child put the focus distance where four times it belongs.

Your child put the directrix on the same side of the vertex as the focus.

What to say

Ask: if 4p = 12, what is p?

Ask: if p = 3, what number goes in the equation?

Ask: which side is the focus on, and where must the line go?

Questions parents ask

What is the most common mistake with parabolas: focus, directrix and equations?

Your child used the whole number in the equation as the distance to the focus, instead of a quarter of it.

How can I help my child with parabolas: focus, directrix and equations?

Ask: if 4p = 12, what is p?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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