A parabola is the set of all points in the plane that are equidistant from a fixed point called the _________ and a fixed line called the ____________ of the parabola.

Check back soon!

The graph of the equation $x^{2}=4 p y$ is a parabola with focus $F($ __________ , ___________ ) and directrix $y=$ So the graph of $x^{2}=12 y$ is a parabola with focus $F=$ (______________ , ________) and directrix $x=$ _____________

Check back soon!

The graph of the equation $y^{2}=4 p x$ is a parabola with focus $F($____________ , ___________ )and directrix $x=$ _____________ So the graph of $y^{2}=12 x$ is a parabola with focus $F$ ( _________ , _________ ) and directrix $x=$ ______________ .

Check back soon!

Label the focus, directrix, and vertex on the graphs given for the parabolas

a. $x^{2}=12 y$

b. $y^{2}=12 x$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$y^{2}=2 x$$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$y^{2}=-\frac{1}{4} x$$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$x^{2}=-6 y$$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$2 x^{2}=y$$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$y^{2}-8 x=0$$

Ankit G.

Numerade Educator

Match the equation with the graphs labeled $\mathbf{I},$ II, III, $\mathrm{IV}$ V and VI. Give reasons for your answers.

$$12 y+x^{2}=0$$

Ankit G.

Numerade Educator

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x^{2}=8 y$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x^{2}=-4 y$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$y^{2}=-24 x$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$y^{2}=16 x$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$y=-\frac{1}{8} x^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x=2 y^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x=-2 y^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$y=\frac{1}{4} x^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$5 y=x^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$9 x=y^{2}$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x^{2}+12 y=0$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$x+\frac{1}{5} y^{2}=0$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$5 x+3 y^{2}=0$$

Check back soon!

An equation of a parabola is given.

(a) Find the focus, directrix, and focal diameter of the parabola.

(b) Sketch a graph of the parabola and its directrix.

$$8 x^{2}+12 y=0$$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F(0,6)$

Ankit G.

Numerade Educator

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F\left(0,-\frac{1}{4}\right)$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F(-8,0)$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F(5,0)$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F\left(0,-\frac{3}{4}\right)$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus: $F\left(-\frac{1}{12}, 0\right)$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $x=-4$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $y=\frac{1}{2}$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $y=\frac{1}{10}$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $x=-\frac{1}{8}$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $x=\frac{1}{20}$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix: $y=-5$

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus on the positive $x$ -axis, 2 units away from the directrix

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focus on the negative $y$ -axis, 6 units away from the directrix

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Opens downward with focus 10 units away from the vertex

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Opens upward with focus 5 units away from the vertex

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Directrix has $y$ -intercept 6

Check back soon!

Find an equation for the parabola that has its vertex at the origin and satisfies the given

condition(s).

Focal diameter 8 and focus on the negative $y$ -axis

Check back soon!

(a) Find equations for the family of parabolas with the given description.

(b) Draw the graphs.

What do you conclude?

The family of parabolas with vertex at the origin and with directrixes $y=\frac{1}{2}, y=1, y=4,$ and $y=8$

Ankit G.

Numerade Educator

Find an equation of the parabola whose graph is shown.

(a) Find equations for the family of parabolas with the given description.

(b) Draw the graphs.

What do you conclude?

The family of parabolas with vertex at the origin, focus on the positive $y$ -axis, and with focal diameters $1,2,4,$ and 8

Ankit G.

Numerade Educator

Parabolic Reflector A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus, and the focal diameter is $12 \mathrm{cm}$.

a. Find an equation of the parabola.

b. Find the diameter $d(C, D)$ of the opening, $20 \mathrm{cm}$ from the vertex.

Check back soon!

Satellite Dish A reflector for a satellite dish is parabolic in cross section, with the receiver at the focus $F$. The reflector is $1 \mathrm{ft}$ deep and $20 \mathrm{ft}$ wide from rim to rim (See the figure). How far is the receiver from the vertex of the parabolic reflector?

Check back soon!

Suspension Bridge In a suspension bridge the shape of the suspension cables is par The bridge shown in the figure has towers that are 600 m apart, and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the vertex. [Note: This equation is used to find the length of cable needed in the construction of the bridge.]

Ankit G.

Numerade Educator

Reflecting Telescope The Hale telescope at the Mount Palomar Observatory has a 200 -in. mirror, as shown in the figure. The mirror is constructed in a parabolic shape that collects light from the stars and focuses it at the prime focus, that is, the focus of the parabola. The mirror is 3.79 in. deep at its center. Find the focal length of this parabolic mirror, that is, the distance from the vertex to the focus.

Check back soon!

Discuss - Write: Parabolas in the Real World Several examples of the uses of

parabolas are given in the text. Find other situations in real life in which parabolas occur. Consult a scientific encyclopedia in the reference section of your library, or search the Internet.

Check back soon!

Discuss: Light Cone from a Flashlight A flashlight is held to form a lighted area on the ground, as shown in the figure. Is it possible to angle the flashlight in such a way that the boundary of the lighted area is a parabola? Explain your answer.

Check back soon!