ACT Math Question (Circles)

Test Preparation ACT Preparation
1

One of the problems in an official ACT practice test says:

A circle in the standard (x,y) coordinate plane is tangent to the x-axis at 5 and tangent to the y-axis at 5. Which of the following is an equation of the circle?

A. x^2+y^2=5
B. x^2+y^2=25
C. (x-5)^2+(y-5)^2=5
D. (x-5)^2+(y-5)^2=25
E. (x+5)^2+(y+5)^2=25

The correct answer is D, and I understand why, but I’m not sure why B is incorrect. Both B and D touch the x and y-axis at 5, so why is B incorrect? The answer explanation says that “B is a circle centered at (0,0) instead of (5,5)” but I don’t understand why the vertex has to be (5,5) is the one at (0,0) touches 5 on both axes. I also know that a tangent to a circle is perpendicular to the radius. Don’t both equations from B and D satisfy that?

Also, I’m fully aware that the ACT always has 1 and only 1 correct answer, but I’m struggling to figure out why B is incorrect. Any help would be greatly appreciated. Thanks!

2

Can you draw both B and D on a piece of paper? For B, you can draw the tangent line Y=5 and X=5, but it does not mean that it is tangent to the x-axis at 5 and y-axis at 5. For D, x=0 and y=0 are the tangent lines, but the circle touches the tangent line at 5. I hope I can explain better.

3

@annamom OH I get it! I can’t seem to figure out how to attach images on here, but yes, I see how it isn’t tangent to the x and y-axis. Thank you so much!!