Hello,
Can you please tell me how to solve this:
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
OA: C
I am thinking that in I, the y-intercept is 1 and the slope is -1. However, I don't know how to tell from this whether I intersects the circle in 2 points. Thanks a lot.
- Sri
Lines that intersect the circle in 2 points
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Any line that passes through the interior of the circle will intersect the circle at two points.gmattesttaker2 wrote:Hello,
Can you please tell me how to solve this:
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
OA: C
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).
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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