Question

nts) In many cases, it can be easier to describe a curve with Cartesian coordinates. Other times, polar coordinates may be easier. Below, four curves are described in words, and four choices of equations are given -- two are in Cartesian form and two in polar form. Match each description with the correct curve. A. A line through the origin that makes an angle of π/6 with the positive x-axis. B. A vertical line through the point (3, 3). C. A circle with radius 5 and cent

Answer 1

The pairs are matched

Explanation:

A. A line through the origin that makes an angle of
`\pi/6` with the positive x-axis.

Given a line through the origin that makes an angle of
`\pi/6` with the positive x-axis. The angle which the line makes with the x-axis is
`\pi/6`.

• Therefore,
  `\theta = \pi/6`

B. A vertical line through the point (3, 3).

If a line passes through the point (3,3), x=3 and y=3. The vertical line through the point (3,3) is x=3

C. Given a circle center (h,k) and a center r, the standard form of the equation of the circle is given as:

`(x-h)^2+(y-k)^2=r^2`

Therefore, for a circle with radius 5 and center (2, 3), the standard form equation is:

• 
  `(x-2)^2+(y-3)^2=25`

D. A circle centered at the origin with radius.

For a circle centered at the origin with radius r=4.

The radius of the circle is 4 units.

• r=4