A conic (or conic section) is a smooth curve formed when a plane intersects a pair of right circular cones placed pointtopoint. 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.
Figure 1 [Source: Wikipedia  Conic Section] 

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.
Problem Statement 

Classify and list the attributes of the conic \(x^24x4y=0\).
Solution 

video by Krista King Math 

close solution

Log in to rate this practice problem and to see it's current rating. 

Problem Statement 

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

video by PatrickJMT 

close solution

Log in to rate this practice problem and to see it's current rating. 

Problem Statement 

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

video by MIP4U 

close solution

Log in to rate this practice problem and to see it's current rating. 

Problem Statement 

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

video by MIP4U 

close solution

Log in to rate this practice problem and to see it's current rating. 

Problem Statement 

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

video by PatrickJMT 

close solution

Log in to rate this practice problem and to see it's current rating. 

You CAN Ace Calculus
external links you may find helpful 

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

MultiVariable Calculus 

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.
 
free ideas to save on books 

Help Keep 17Calculus 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. 