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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
Expert Reply
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Question Stats:
25% (01:41) correct
75% (02:13) wrong based on 8 sessions
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In the xy plane, the point of intersection of the line \(–3y = 12 +2x\) 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
[#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 𝑅^2 = 𝑥^2 + 𝑦^2
Given equation of circle is 𝑥^2 + 𝑦^2 = 25,
So, radius of circle is 𝑅 = 5 units. So, circle would be as shown in the figure below.
Now line −3𝑦 = 12 + 2𝑥. Let’s express it in the slope-intercept form, we have \(y=-\frac{2}{3} x-4\)
Here slope is negative and 𝑦 intercept is -4. And 𝑥 intercept is -12.
This is a falling line, crossing 𝑦-axis below 𝑥 −axis at point (0, -4). And crossing 𝑥 −axis 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 𝑅^2 = 𝑥^2 + 𝑦^2
Given equation of circle is 𝑥^2 + 𝑦^2 = 25,
So, radius of circle is 𝑅 = 5 units. So, circle would be as shown in the figure below.
Now line −3𝑦 = 12 + 2𝑥. Let’s express it in the slope-intercept form, we have \(y=-\frac{2}{3} x-4\)
Here slope is negative and 𝑦 intercept is -4. And 𝑥 intercept is -12.
This is a falling line, crossing 𝑦-axis below 𝑥 −axis at point (0, -4). And crossing 𝑥 −axis 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
