The graph of r=-14 cos theta has which of the following characteristics?

Question

asked Jan 20, 2020 67.0k views

2 Answers

Mofaggol Hoshen · Answer 1 · 2020-01-25T10:58:40+0000

Answer:

A

Explanation:

Use formulas:

r=√(x^2+y^2),

$\cos \theta=(x)/(√(x^2+y^2)).$

Substitute them into the equation
$r=-14\cos \theta:$

$√(x^2+y^2)=-14\cdot (x)/(√(x^2+y^2)).$

Multiply this equation by
√(x^2+y^2):

x^2+y^2=-14x.

Now rewrite this equation as

$x^2+14x+y^2=0,\\ \\x^2+14x+49-49+y^2=0,\\ \\(x+7)^2+y^2=49.$

This is the equation of the circle with center at point (-7,0) and radius r=7 (diameter 14).