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Conic Sections Classifying Conic Sections NOTES The four conic sections are the circle, ellipse, parabola, and hyperbola. They can all be obtained by slicing a right circular cone at different angles.

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Conic Section Standard Forms Circle: x2+y2=a2 Ellipse: x2/a2 + y2/b2 = 1. Hyperbola: x2/a2 – y2/b2 = 1. Parabola: y2=4ax when a>0.

If B2 -4AC < 0, the conic is a circle, or an ellipse. If B2 - 4AC = 0, the conic is a parabola. Another way to classify conics has to do with the product of A and C.

The equation of a hyperbola is in general form if it is in the form A x 2 + B y 2 + C x + D y + E = 0 , A x 2 + B y 2 + C x + D y + E = 0 , where A and B have opposite signs.

Steps to Identify Conic Sections From General Form If A and C are non zero and equal, and both have the same sign, then it will be a circle. If A and C are non zero and unequal, and have the same sign, then it will be an ellipse. If A or C is zero, then it will be a parabola.

Conic Sections Equations Conic section NameEquation when the centre is at the Origin, i.e. (0, 0)Circlex2 + y2 = r2; r is the radiusEllipse(x2/a2) + (y2/b2) = 1Hyperbola(x2/a2) – (y2/b2) = 1Parabolay2 = 4ax, where a is the distance from the origin to the focus

The discriminant (B2-4AC) is used to determine which conic section will result. If the discriminant is less than zero we have a circle (if A = C) or an ellipse; if the discriminant is equal to zero we have a parabola; if the discriminant is greater than zero we have a hyperbola.

0:45 3:33 Determining What Type of Conic Section from General Form - YouTube YouTube Start of suggested clip End of suggested clip And if this is the case we will have an ellipse. So this first example we have a equals one and cMoreAnd if this is the case we will have an ellipse. So this first example we have a equals one and c equals.

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© Copyright 1997-2025
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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
Industries
Forms in Spanish
Localized Forms
State-specific Forms
Forms Kit
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232