To find: Transform the polar equation r = 2 to rectangular equation. Then identify and match the graph given.
Solution:
The graph of r = 2 is the equation of circle x2 + y2 = 22 with center (0, 0) and radius 2.
From the given graph, option E satisfies the condition of circle.
Given:
It is asked to transform the polar equation r = 2 to rectangular equation and match the graph.
Convert the polar equation to a rectangular equation = 2.
Formula used:
(x, y) = (r cosθ, r sinθ)x2 + y2 = r2
Consider = 2,
Squaring on both the sides,
r2 = 4x2 + y2 = 4x2 + y2 = 22
The above is an equation of circle with center (0, 0) and radius 2.
The graph of r = 2 is the equation of circle (x + 2)2 + y2 = 22 with center (0, 0) and radius 2.
Precalculus Enhanced with Graphing Utilities
Precalculus
Calculus: Early Transcendentals (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Glencoe Math Accelerated, Student Edition
Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)