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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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GPA: 3.39
A circle with center O and radius 5 is shown in the xy-plane. Lines th
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Updated on: 26 Jul 2022, 09:23
Updated on: 26 Jul 2022, 09:23
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Question Stats:
66% (02:51) correct
33% (02:36) wrong based on 3 sessions
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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
Originally posted by GeminiHeat on 26 Jul 2022, 02:11.
Last edited by Carcass on 26 Jul 2022, 09:23, edited 1 time in total.
Last edited by Carcass on 26 Jul 2022, 09:23, edited 1 time in total.
UPDATED
Re: A circle with center O and radius 5 is shown in the xy-plane. Lines th
[#permalink]
26 Jul 2022, 08:35
26 Jul 2022, 08:35
1
Solution -
In co-ordinate geometry, create your own diagrams and mark the axis.
On the x-axis, draw a circle with a radius of 5 and centre at (0, 0).
It will cut the x-axis at 5 and -5 and the y-axis at 5 and -5.
The next step is to plot the three given lines given in the question.
(I) y = -x +1
Plug-in the value, x = 0, then you will get y = 1. So this line cuts the y-axis at 1.
Plug-in the value, y = 0, then you will get x = 1. So this line cuts the x-axis at 1.
This line, when extended on both sides will cut the circle at two distinct points.
(II) y = 2x + 1
Plug-in the value, x = 0, then you will get y = 1. So this line cuts the y-axis at 1.
Plug-in the value, y = 0, then you will get x = -1/2. So this line cuts the x-axis at -1/2.
Similarly, we plot this line and you will see that it will cut the circle at two points too.
(III) y = (1/2)x - 6
Plug-in the value, x = 0, then you will get y = -6. So this line cuts the y-axis at -6.
Plug-in the value, y = 0, then you will get x = 12. So this line cuts the x-axis at 12.
Hence, this line cuts the y-axis at -6 and the x-axis at 12. It is outside the circle and hence doesn't cut the circle.
Hence, the correct answer is (C)
In co-ordinate geometry, create your own diagrams and mark the axis.
On the x-axis, draw a circle with a radius of 5 and centre at (0, 0).
It will cut the x-axis at 5 and -5 and the y-axis at 5 and -5.
The next step is to plot the three given lines given in the question.
(I) y = -x +1
Plug-in the value, x = 0, then you will get y = 1. So this line cuts the y-axis at 1.
Plug-in the value, y = 0, then you will get x = 1. So this line cuts the x-axis at 1.
This line, when extended on both sides will cut the circle at two distinct points.
(II) y = 2x + 1
Plug-in the value, x = 0, then you will get y = 1. So this line cuts the y-axis at 1.
Plug-in the value, y = 0, then you will get x = -1/2. So this line cuts the x-axis at -1/2.
Similarly, we plot this line and you will see that it will cut the circle at two points too.
(III) y = (1/2)x - 6
Plug-in the value, x = 0, then you will get y = -6. So this line cuts the y-axis at -6.
Plug-in the value, y = 0, then you will get x = 12. So this line cuts the x-axis at 12.
Hence, this line cuts the y-axis at -6 and the x-axis at 12. It is outside the circle and hence doesn't cut the circle.
Hence, the correct answer is (C)
Re: A circle with center O and radius 5 is shown in the xy-plane. Lines th
[#permalink]
26 Jul 2022, 09:24
26 Jul 2022, 09:24
Expert Reply
Updated the first post
