Question

Select the correct answer from each drop-down menu.

x^2+y^2=25 is written in polar form as__
A) r=5
B) r=25
C) a=5
D) a=25

θ = 225º is written in rectangular form as__
A) y=1
B) y=-1
C) y=x
D) y=-x

Answer 1

a) Option A: r = 5

b) Option C: y = x

Explanation:

a) First, we know that a circle centered at the origin of radius R is written as:

x^2 + y^2 = R^2

Then x^2+y^2=25 can be rewritten as:

x^2 + y^2 = 5^2

This is a circle of radius 5.

Then in polar form, this can be written as:

r = 5

b) Now we have the angle 225°

For rectangular coordinates (x, y)

The correspondent value of θ is given by:

Tan(θ) = y/x

In this case, we have θ = 225°

Then:

Tan(225°) = 1 = y/x

This can be rewritten as x = y

Then the correct option is C) y = x