GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A circle with center O and radius 5 is shown in the xy-plane. Lines th
[#permalink]
Updated on: 26 Jul 2022, 09:23
Updated on: 26 Jul 2022, 09:23
Expert Reply
2
Bookmarks
00:00
Question Stats:
66% (02:51) correct
33% (02:36) wrong based on 3 sessions
Hide Show timer Statistics
Attachment:
GRE circle (10).jpg [ 36.37 KiB | Viewed 1671 times ]
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
