violetsplash wrote:
A circle with center O and radius 5 is shown in the xy-plane. Lines that intersect the circle in 2 points include which of the following ?
I. y = -x +1
II. y = 2x + 1
III. y = (1/2)x - 6
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III
Any line that passes through the interior of the circle will intersect the circle at two points.
The x-intercepts of the circle are -5 and 5.
The y-intercepts of the circle are -5 and 5.
I. y = -x + 1
II. y = 2x + 1
Each of these lines has a y-intercept between -5 and 5.
Thus, each line must pass through the interior of the circle.
Eliminate any answer choice that does not include both I and II (A, B and D).
III. y = (1/2)x - 6
Here, the y-intercept = -6.
To determine the x-intercept, substitute y=0 and solve for x:
0 = (1/2)x - 6
x=12.
Since the x-intercept = 12 and the y-intercept = -6, this line does not pass through the interior of the circle.
Eliminate any remaining answer choice that includes III (E).
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