Question

Find an equation equivalent to r = 6secx in rectangular coordinates and describe the graph of the equation.

A. x ·
`\sqrt{x^(2) + y^(2) }` = 6; circle with radius 6

B.
`\sqrt{x^(2) + y^(2) }` = 6; circle with radius 6

C. x = 6; straight vertical line

D. y = 6; straight horizontal line

Answer 1

C. x = 6; straight vertical line

Explanation:

you have the following equation in polar coordinates:

`r=6sec(\theta)`

To find the equation in rectangular coordinates you take into account the following transformations:

`r=√(x^2+y^2)\\\\x=rcos(\theta)\\\\`

Next, you replace and obtain:

`r=6sec(\theta)\\\\r=(6)/(cos(\theta))\\\\rcos(\theta)=6`

but, you have that x = rcos(θ), hence, x = 6

C. x = 6; straight vertical line