Question

Determine the coordinates of the center and the radius of the circle rcsc(θ)=−38. Convert to a rectangular equation if necessary. (Use symbolic notation and fractions where needed. Give your answer as a comma separated list of a point's coordinates in the form (∗,∗)) the coordinates of the center:

Answer 1

To determine the center and radius of the circle with the given polar equation, we need to convert it to rectangular form. The center coordinates are (-38, 0) and the radius is 38.

Step-by-step explanation:

To determine the coordinates of the center and the radius of the circle, we need to convert the given polar equation to rectangular form. The given polar equation is rcsc(θ) = -38. We know that the rectangular coordinates (x, y) can be expressed in terms of polar coordinates (r, θ) as x = rcos(θ) and y = rsin(θ). So we can rewrite the polar equation as x/cos(θ) = -38. Simplifying further, we get x = -38cos(θ).

Since we want to express the answer in the form of (∗, ∗), we need to find the coordinates of the center. The center of the circle is (h, k) and is given by (x, y) = (-38cos(θ), 0). So the coordinates of the center are (-38, 0).

The radius of the circle is given by the absolute value of r, which in this case is |-38| = 38. Therefore, the radius of the circle is 38. The coordinates of the center and the radius of the circle in rectangular form are (-38, 0) and 38, respectively.