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.
In the xy plane, the point of intersection of the line 3y = 12 +2x an
[#permalink]
06 Sep 2023, 09:23
06 Sep 2023, 09:23
Expert Reply
00:00
Question Stats:
25% (01:41) correct
75% (02:13) wrong based on 8 sessions
Hide Show timer Statistics
In the xy plane, the point of intersection of the line \(โ3y = 12 +2x\) and the circle \(x^2 + y^2 = 25\) lie in which quadrant?
Indicate all that apply
A. I
B. II
C. III
D. IV
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Indicate all that apply
A. I
B. II
C. III
D. IV
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: In the xy plane, the point of intersection of the line 3y = 12 +2x an
[#permalink]
14 Sep 2023, 15:42
14 Sep 2023, 15:42
Expert Reply
OE
Equation of a circle, having origin as its centre, is in the form ๐ ^2 = ๐ฅ^2 + ๐ฆ^2
Given equation of circle is ๐ฅ^2 + ๐ฆ^2 = 25,
So, radius of circle is ๐ = 5 units. So, circle would be as shown in the figure below.
Now line โ3๐ฆ = 12 + 2๐ฅ. Letโs express it in the slope-intercept form, we have \(y=-\frac{2}{3} x-4\)
Here slope is negative and ๐ฆ intercept is -4. And ๐ฅ intercept is -12.
This is a falling line, crossing ๐ฆ-axis below ๐ฅ โaxis at point (0, -4). And crossing ๐ฅ โaxis at (-12,0)
So, the line is crossing the circle in quadrant III and IV.
Ans. (C and D)
Equation of a circle, having origin as its centre, is in the form ๐ ^2 = ๐ฅ^2 + ๐ฆ^2
Given equation of circle is ๐ฅ^2 + ๐ฆ^2 = 25,
So, radius of circle is ๐ = 5 units. So, circle would be as shown in the figure below.
Now line โ3๐ฆ = 12 + 2๐ฅ. Letโs express it in the slope-intercept form, we have \(y=-\frac{2}{3} x-4\)
Here slope is negative and ๐ฆ intercept is -4. And ๐ฅ intercept is -12.
This is a falling line, crossing ๐ฆ-axis below ๐ฅ โaxis at point (0, -4). And crossing ๐ฅ โaxis at (-12,0)
So, the line is crossing the circle in quadrant III and IV.
Ans. (C and D)
Re: In the xy plane, the point of intersection of the line 3y = 12 +2x an
[#permalink]
04 Dec 2023, 04:44
04 Dec 2023, 04:44
Carcass is there any other method to check without drawing the graph? and i think X-int is -6
