\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{\mathrm{sec} } \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{\mathrm{arccot} } \) \( \newcommand{\arcsec}{\mathrm{arcsec} } \) \( \newcommand{\arccsc}{\mathrm{arccsc} } \) \( \newcommand{\sech}{\mathrm{sech} } \) \( \newcommand{\csch}{\mathrm{csch} } \) \( \newcommand{\arcsinh}{\mathrm{arcsinh} } \) \( \newcommand{\arccosh}{\mathrm{arccosh} } \) \( \newcommand{\arctanh}{\mathrm{arctanh} } \) \( \newcommand{\arccoth}{\mathrm{arccoth} } \) \( \newcommand{\arcsech}{\mathrm{arcsech} } \) \( \newcommand{\arccsch}{\mathrm{arccsch} } \)

17Calculus - Conics

Limits

Using Limits

Limits FAQs

Derivatives

Graphing

Applications

Derivatives FAQs

Integrals

Trig Integrals

Area/Volume

Applications

Infinite Series

Applications

Tools

Parametrics

Conics

Polar Coordinates

Laplace Transforms

Tools

Calculus Tools

Additional Tools

Articles

A conic (or conic section) is a smooth curve formed when a plane intersects a pair of right circular cones placed point-to-point. The angle of the plane measured with respect to the axis running through the point of the cones, determines the type of conic that is formed.

There are three types of curves.
1. Parabolas
2. Ellipses (circles are special cases of ellipses and are sometimes listed as a fourth type)
3. Hyperbolas

Parabolas and hyperbolas are very similar and are easy to confuse. One difference is that there are a pair of curves in the case of a hyperbola but parabolas occur as a single curve.

The general equation for all these equations is \(Ax^2+Bxy+Cy^2+Dx+Ey+F=0\). There are a lot of differences in this equation for each curve.
We discuss each of the three types on separate pages. Once you have gone over that material and practiced some specific problems, feel free to come back here and try these practice problems. We do not tell you what type of curves these are, so you get to figure it out. Instructors will often put these types of problems on exams.
We suggest you start with parabolas, since you have probably seen them before in precalculus.

Practice

Classify and list the attributes of the conic \(x^2-4x-4y=0\).

Problem Statement

Classify and list the attributes of the conic \(x^2-4x-4y=0\).

Solution

1593 video

video by Krista King Math

close solution
Graph \( x^2 + 2y^2 - 6x + 4y + 7 = 0 \).

Problem Statement

Graph \( x^2 + 2y^2 - 6x + 4y + 7 = 0 \).

Solution

1603 video

video by PatrickJMT

close solution
Graph \( 4x^2 - y^2 = 16 \).

Problem Statement

Graph \( 4x^2 - y^2 = 16 \).

Solution

1608 video

video by MIP4U

close solution
Graph \( -x^2 + 4y^2 - 2x - 16y + 11 = 0 \).

Problem Statement

Graph \( -x^2 + 4y^2 - 2x - 16y + 11 = 0 \).

Solution

1609 video

video by MIP4U

close solution
Graph \( 4x^2 + y^2 = 16 \).

Problem Statement

Graph \( 4x^2 + y^2 = 16 \).

Solution

1602 video

video by PatrickJMT

close solution

conics 17calculus youtube playlist

You CAN Ace Calculus

Topics You Need To Understand For This Page

Related Topics and Links

To bookmark this page and practice problems, log in to your account or set up a free account.

Calculus Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations Topics Listed Alphabetically

Precalculus Topics Listed Alphabetically

Search Practice Problems

Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.

memorize to learn

Get great tutoring at an affordable price with Chegg. Subscribe today and get your 1st 30 minutes Free!

The 17Calculus and 17Precalculus iOS and Android apps are no longer available for download. If you are still using a previously downloaded app, your app will be available until the end of 2020, after which the information may no longer be available. However, do not despair. All the information (and more) is now available on 17calculus.com for free.

Do NOT follow this link or you will be banned from the site!

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.

We use cookies on this site to enhance your learning experience.

17calculus

Copyright © 2010-2020 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

mathjax.org
Real Time Web Analytics
17Calculus
We use cookies to ensure that we give you the best experience on our website. By using this site, you agree to our Website Privacy Policy.