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In the xy plane, the point of intersection of the line 3y = 12 +2x an
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06 Sep 2023, 09:23
06 Sep 2023, 09:23
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24% (01:28) correct
76% (02:21) wrong based on 25 sessions
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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
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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
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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
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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
