Let $x=a+k \cos t$ and $y=b+k \sin t$ parameterize a circle, with $a

Name: Let $x=a+k \cos t$ and $y=b+k \sin t$ parameterize a circle, with $a<0, b<0, k<a$, and $k<b$. What quadrant does the circle lie in? A) The second B) The third C) The fourth D) The first
Brand: Quizplus
Rating: 4.7 (35 reviews)

Question

Let $x=a+k \cos t$ and $y=b+k \sin t$ parameterize a circle, with $a<0, b<0, k<a$, and $k<b$. What quadrant does the circle lie in?
A) The second
B) The third
C) The fourth
D) The first

Quizplus · Accepted Answer

The center of the circle is at $(a, b)$, which is in the third quadrant since both $a$ and $b$ are negative. The radius $k$ is less than the absolute values of both $a$ and $b$, ensuring the entire circle lies within the third quadrant.

Let x=a+kcos⁡tx=a+k \cos tx=a+kcost And y=b+ksin⁡ty=b+k \sin ty=b+ksint Parameterize a Circle, With a<0,b<0,k<aa<0, b<0, k<aa<0,b<0,k<a

Let $x=a+k \cos t$ And $y=b+k \sin t$ Parameterize a Circle, With $a<0, b<0, k<a$