Question

The equations of three distinct circles are listed below. Using complete sentences, explain which of the three circles would intersect the x-axis only. Justify your answer. (3 points: 1 point for the answer and 2 points for the justification)
Circle A: (x – 9)2 + (y – 3)2 = 25
Circle B: (x –7)2 + (y + 2)2 = 49
Circle C: (x + 2)2 + y2 = 16

Answer 1

How far have you gotten with this question before getting stuck?

Answer 2

secret lies in the formula itself.

When rearranged into this structure (luckily you are already in the right structure)

(x-a)^2 + (y-b)^2=r^2
a is the middle on x axis, b is middle on the y axis and r is the radius

if the middle is further from the y axis than the radius of the circle, the circle doesnt intersect the y axis as the circle isnt large enough to reach.

so for the first equation mid point is at (x=9,y=3) and radius is 5. so as the middle is more than 5 away from the y axis it doesnt intersect it

so for the second equation mid point is at (x=7,y=-2) and radius is 7. so it just touches the y axis and dosent intersect it

and for the third equation the mid point is (x=-2,y=0) and the radius is 4, so as the middle is only 2 away from the y axis it does intersect it

Hope that helps..