Question

Which of the following circles have their centers on the x-axis? Check all that apply.

Answer 1

Answer:

$Circles\thinspace (x - 0)^2 + (y - 0)^2 = 72\thinspace and \thinspace (x - 4)^2 + (y - 0)^2 = 74\text{ have their centers on the x-axis.}$    

Step-by-step explanation:

Given the equations of circle. we have to find the equation of circle whose center on the x-axis.

The standard form of equation of circle is  

$(x-h)^2+(y-k)^2=r^2$

where (h,k) is center and r is radius.

Given equations are

$(x - 2)^2 + (y + 3)^2 = 2$            Center:(2,-3)

$(x - 0)^2 + (y - 3)^2 = 23$           Center:(0,3)

$(x - 0)^2 + (y - 0)^2 = 72$           Center:(0,0)

$(x - 4)^2 + (y - 0)^2 = 74$           Center:(4,0)

The points with ordinate 0 lies on x-axis

Hence, $Circles\thinspace (x - 0)^2 + (y - 0)^2 = 72\thinspace and \thinspace (x - 4)^2 + (y - 0)^2 = 74\text{ have their centers on the x-axis.}$