Conic Sections Overview Math Example 1

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Example 1

easy
Identify the type of conic section: x29+y29=1\frac{x^2}{9} + \frac{y^2}{9} = 1.

Solution

  1. 1
    The equation has the form x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 with both terms positive (addition).
  2. 2
    Since a2=b2=9a^2 = b^2 = 9, we have a=b=3a = b = 3.
  3. 3
    An ellipse with a=ba = b is a circle of radius 33 centered at the origin.

Answer

Circle with radius 3\text{Circle with radius } 3
A circle is a special case of an ellipse where both semi-axes are equal (a=ba = b). The four conic sections — circle, ellipse, parabola, and hyperbola — are all cross-sections of a cone, distinguished by the angle at which the cutting plane intersects the cone.

About Conic Sections Overview

The four curves—circle, ellipse, parabola, and hyperbola—obtained by slicing a double cone with a plane at different angles.

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More Conic Sections Overview Examples

Example 2 medium

Classify the conic given by [formula].

Example 3 medium

Classify each equation: (a) [formula], (b) [formula], (c) [formula].

Example 4 hard

The general equation [formula] represents a circle only when [formula] takes a specific value. Find

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