\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \)

You CAN Ace Calculus

Topics You Need To Understand For This Page

Related Topics and Links

17Calculus Subjects Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations

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.

effective study techniques

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 solution 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 solution video

video by PatrickJMT

close solution

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

Problem Statement

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

Solution

1608 solution 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 solution video

video by MIP4U

close solution

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

Problem Statement

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

Solution

1602 solution video

video by PatrickJMT

close solution
Real Time Web Analytics