**ERIC Number:**EJ875466

**Record Type:**Journal

**Publication Date:**2004

**Pages:**11

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

Finding Equations of Tangents to Conics

Baloglou, George; Helfgott, Michel

AMATYC Review, v25 n2 p35-45 Spr 2004

A calculus-free approach is offered for determining the equation of lines tangent to conics. Four types of problems are discussed: line tangent to a conic at a given point, line tangent to a conic passing through a given point outside the conic, line of a given slope tangent to a conic, and line tangent to two conics simultaneously; in each case, a comparison to the standard calculus method is made by way of specific examples. Extending an idea of Descartes, this calculus-free approach is based on the fact that a quadratic has a double root if and only if its discriminant is equal to zero. It should be appropriate for both precalculus and calculus students.

Descriptors: Calculus, Equations (Mathematics), Mathematics Instruction, Teaching Methods, Mathematics Skills, Mathematical Concepts, College Mathematics, Two Year Colleges

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A