Graphing Techniques

Lesson 4: Conics

Introduction

Conics refer to graphs with polynomial equations in x or y with maximum power 2.

Note: The standard equations of conics are in completed square form.

(A) Parabola

(B) Ellipse / Circle

Note: When c = d, we have a circle with radius c.

(C) Hyperbola

The standard equations of a hyperbola are:

(a, b) = centre of the hyperbola

The equations of the asymptotes are:

Example 1

Identify the following graphs and sketch them, labelling the necessary features.

(a)

(b)

Solution

(a)

O

(b)

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