Which of the following circles lie completely within the fourth quadrant?Check all that apply.

Accepted Solution

Answer:C and DStep-by-step explanation:The fourth quadrant is where all the points are in the form (positive, negative).The center and radius of [tex](x-h)^2+(y-k)^2=r^2[/tex] is (h,k) and r, respectively.Let's look at the centers and the radius of each of these choices:A) This one has center (4,-2) and radius [tex]\sqrt{32} \approx 5.7[/tex].If you add 5.7 to -2 you get a positive number and we needed it negative.Not this choice; moving on.B) This one has center (-3,2) and radius [tex]\sqrt{25}=5[/tex].The center is not even in quadrant 4; moving on.C) This one has a center (3,-4) and radius 1.Add 1 to 3 you get 4.Subtract 1 from 3 you get 2. Those x's are positive so that looks good so far.Add 1 to -4 you get -3.Subtract 1 from -4 you get -5.Those y's are negative so that looks good.This circle is in quadrant 4 and doesn't go outside it.D) This one has center (5,-7) and radius 4.Add 4 to 5 you get 9.Subtract 4 from 5 you get 1.Positive x's is good.Add 4 to -7 you get -3.Subtract 4 from -7 you get -11.Those are negative so that looks good.