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).

In the two cases below, did you set Y = 0 to find Y-intercept and X = 0 to find X-intercept ? Do we need to test both Y and X intercept to detrmine wether question is correct or not ? thank you and have a nice weekend

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).