<< Chapter < Page Chapter >> Page >

( y + 4 ) 2 = 16 ( x + 4 )

Got questions? Get instant answers now!

y 2 + 12 x 6 y + 21 = 0

( y 3 ) 2 = −12 ( x + 1 ) , V : ( 1 , 3 ) ; F : ( 4 , 3 ) ; d : x = 2

Got questions? Get instant answers now!

x 2 4 x 24 y + 28 = 0

Got questions? Get instant answers now!

5 x 2 50 x 4 y + 113 = 0

( x 5 ) 2 = 4 5 ( y + 3 ) , V : ( 5 , 3 ) ; F : ( 5 , 14 5 ) ; d : y = 16 5

Got questions? Get instant answers now!

y 2 24 x + 4 y 68 = 0

Got questions? Get instant answers now!

x 2 4 x + 2 y 6 = 0

( x 2 ) 2 = −2 ( y 5 ) , V : ( 2 , 5 ) ; F : ( 2 , 9 2 ) ; d : y = 11 2

Got questions? Get instant answers now!

y 2 6 y + 12 x 3 = 0

Got questions? Get instant answers now!

3 y 2 4 x 6 y + 23 = 0

( y 1 ) 2 = 4 3 ( x 5 ) , V : ( 5 , 1 ) ; F : ( 16 3 , 1 ) ; d : x = 14 3

Got questions? Get instant answers now!

x 2 + 4 x + 8 y 4 = 0

Got questions? Get instant answers now!

Graphical

For the following exercises, graph the parabola, labeling the focus and the directrix.

( y 2 ) 2 = 4 3 ( x + 2 )

Got questions? Get instant answers now!

−5 ( x + 5 ) 2 = 4 ( y + 5 )

Got questions? Get instant answers now!

−6 ( y + 5 ) 2 = 4 ( x 4 )

Got questions? Get instant answers now!

y 2 6 y 8 x + 1 = 0

Got questions? Get instant answers now!

x 2 + 8 x + 4 y + 20 = 0

Got questions? Get instant answers now!

3 x 2 + 30 x 4 y + 95 = 0

Got questions? Get instant answers now!

y 2 8 x + 10 y + 9 = 0

Got questions? Get instant answers now!

y 2 + 2 y 12 x + 61 = 0

Got questions? Get instant answers now!

2 x 2 + 8 x 4 y 24 = 0

Got questions? Get instant answers now!

For the following exercises, find the equation of the parabola given information about its graph.

Vertex is ( 0 , 0 ) ; directrix is y = 4 , focus is ( 0 , −4 ) .

x 2 = −16 y

Got questions? Get instant answers now!

Vertex is ( 0 , 0 ) ; directrix is x = 4 , focus is ( −4 , 0 ) .

Got questions? Get instant answers now!

Vertex is ( 2 , 2 ) ; directrix is x = 2 2 , focus is ( 2 + 2 , 2 ) .

( y 2 ) 2 = 4 2 ( x 2 )

Got questions? Get instant answers now!

Vertex is ( −2 , 3 ) ; directrix is x = 7 2 , focus is ( 1 2 , 3 ) .

Got questions? Get instant answers now!

Vertex is ( 2 , 3 ) ; directrix is x = 2 2 , focus is ( 0 , 3 ) .

( y + 3 ) 2 = −4 2 ( x 2 )

Got questions? Get instant answers now!

Vertex is ( 1 , 2 ) ; directrix is y = 11 3 , focus is ( 1 , 1 3 ) .

Got questions? Get instant answers now!

For the following exercises, determine the equation for the parabola from its graph.

( y 2 ) 2 = 1 4 ( x + 2 )

Got questions? Get instant answers now!

( y 3 ) 2 = 4 5 ( x + 2 )

Got questions? Get instant answers now!

Extensions

For the following exercises, the vertex and endpoints of the latus rectum of a parabola are given. Find the equation.

V ( 0 , 0 ) , Endpoints  ( 2 , 1 ) , ( −2 , 1 )

Got questions? Get instant answers now!

V ( 0 , 0 ) , Endpoints  ( −2 , 4 ) , ( −2 , −4 )

y 2 = −8 x

Got questions? Get instant answers now!

V ( 1 , 2 ) , Endpoints  ( −5 , 5 ) , ( 7 , 5 )

Got questions? Get instant answers now!

V ( −3 , −1 ) , Endpoints  ( 0 , 5 ) , ( 0 , −7 )

( y + 1 ) 2 = 12 ( x + 3 )

Got questions? Get instant answers now!

V ( 4 , −3 ) , Endpoints  ( 5 , 7 2 ) , ( 3 , 7 2 )

Got questions? Get instant answers now!

Real-world applications

The mirror in an automobile headlight has a parabolic cross-section with the light bulb at the focus. On a schematic, the equation of the parabola is given as x 2 = 4 y . At what coordinates should you place the light bulb?

( 0 , 1 )

Got questions? Get instant answers now!

If we want to construct the mirror from the previous exercise such that the focus is located at ( 0 , 0.25 ) , what should the equation of the parabola be?

Got questions? Get instant answers now!

A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 12 feet across at its opening and 4 feet deep at its center, where should the receiver be placed?

At the point 2.25 feet above the vertex.

Got questions? Get instant answers now!

Consider the satellite dish from the previous exercise. If the dish is 8 feet across at the opening and 2 feet deep, where should we place the receiver?

Got questions? Get instant answers now!

A searchlight is shaped like a paraboloid of revolution. A light source is located 1 foot from the base along the axis of symmetry. If the opening of the searchlight is 3 feet across, find the depth.

0.5625 feet

Got questions? Get instant answers now!

If the searchlight from the previous exercise has the light source located 6 inches from the base along the axis of symmetry and the opening is 4 feet, find the depth.

Got questions? Get instant answers now!

An arch is in the shape of a parabola. It has a span of 100 feet and a maximum height of 20 feet. Find the equation of the parabola, and determine the height of the arch 40 feet from the center.

x 2 = −125 ( y 20 ) , height is 7.2 feet

Got questions? Get instant answers now!

If the arch from the previous exercise has a span of 160 feet and a maximum height of 40 feet, find the equation of the parabola, and determine the distance from the center at which the height is 20 feet.

Got questions? Get instant answers now!

An object is projected so as to follow a parabolic path given by y = x 2 + 96 x , where x is the horizontal distance traveled in feet and y is the height. Determine the maximum height the object reaches.

2304 feet

Got questions? Get instant answers now!

For the object from the previous exercise, assume the path followed is given by y = −0.5 x 2 + 80 x . Determine how far along the horizontal the object traveled to reach maximum height.

Got questions? Get instant answers now!

Questions & Answers

how to solve the Identity ?
Barcenas Reply
what type of identity
Jeffrey
Confunction Identity
Barcenas
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
Shakeena Reply
by how many trees did forest "A" have a greater number?
Shakeena
32.243
Kenard
how solve standard form of polar
Rhudy Reply
what is a complex number used for?
Drew Reply
It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
Is there any rule we can use to get the nth term ?
Anwar Reply
how do you get the (1.4427)^t in the carp problem?
Gabrielle Reply
A hedge is contrusted to be in the shape of hyperbola near a fountain at the center of yard.the hedge will follow the asymptotes y=x and y=-x and closest distance near the distance to the centre fountain at 5 yards find the eqution of the hyperbola
ayesha Reply
A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?
Sandra Reply
Find the domain of the function in interval or inequality notation f(x)=4-9x+3x^2
prince Reply
hello
Jessica Reply
Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of ?105°F??105°F? occurs at 5PM and the average temperature for the day is ?85°F.??85°F.? Find the temperature, to the nearest degree, at 9AM.
Karlee Reply
if you have the amplitude and the period and the phase shift ho would you know where to start and where to end?
Jean Reply
rotation by 80 of (x^2/9)-(y^2/16)=1
Garrett Reply
thanks the domain is good but a i would like to get some other examples of how to find the range of a function
bashiir Reply
what is the standard form if the focus is at (0,2) ?
Lorejean Reply
Practice Key Terms 4

Get the best Precalculus course in your pocket!





Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Precalculus' conversation and receive update notifications?

Ask