Find the intercepts of the circle. Round to the nearest hundredth, when necessary.
-$$( x - 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$$
A)The two x-intercepts are x = 7 and x = -7, and the two y-intercepts are y = 3 and y = -3.
B)The x-intercept is x = 4, and the y-intercept is y = -9.
C)There are no intercepts.
D)The two x-intercepts are x = 4 and x = -4, and the two y-intercepts are y = 3 and y = -3.

Question

Quizplus · Accepted Answer

To find the intercepts of a circle, you set y=0 to find the x-intercepts and x=0 to find the y-intercepts. For this circle, setting y=0 gives $(x-4)^2 + (5)^2 = 9$, which simplifies to $(x-4)^2 = -16$, which has no real solutions, indicating no x-intercepts. Similarly, setting x=0 gives $(4)^2 + (y-5)^2 = 9$, which simplifies to $(y-5)^2 = -7$, also with no real solutions, indicating no y-intercepts. Therefore, this circle does not intersect the x-axis or the y-axis.

Find the Intercepts of the Circle (x−4)2+(y−5)2=9( x - 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9(x−4)2+(y−5)2=9

Find the Intercepts of the Circle $( x - 4 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$