Question

18. A circle in the standard (x,y) coordinate plane is

tangent to the x-axis at 4 and tangent to the y-axis
at 4. Which of the following is an equation of the
circle?
F. (x – 4)2 + (y – 4)2 = 16
G. (x + 4)2 + (y + 4)2 = 16
H. (x – 4)2 + (y – 4)2 = 4
J. x2 + y2 = 16
K. x2 + y2 = 4

Answer 1

9514 1404 393

Answer:

F

Explanation:

If the circle is tangent to the x-axis at 4, the center lies on the line x=4.

If the circle is tangent to the y-axis at 4, the center lies on the line y=4.

If the center of the circle is (x, y) = (4, 4) and it is tangent to the axes, then the radius is 4.

The standard-form equation of the circle centered at (h, k) with radius r is ...

(x -h)² +(y -k)² = r²

For the values (h, k) = (4, 4) and r = 4, the equation is ...

(x -4)² +(y -4)² = 16 . . . . . . matches choice F