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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 :

Answer:

The pairs are matched

Step-by-step explanation:

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

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

  • Therefore, [tex]\theta = \pi/6[/tex]

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:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

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

  • [tex](x-2)^2+(y-3)^2=25[/tex]

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

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