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Bunuel
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What is the maximum possible distance between the point (-5, 0) and a 05 May 2020, 04:17
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C
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68% (01:15) correct 32% (01:23) wrong based on 189 sessions

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What is the maximum possible distance between the point (-5, 0) and a point on the circle x^2 + y^2 = 4 ?

A. 3
B. 5
C. 7
D. 8
E. 9
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C
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What is the maximum possible distance between the point (-5, 0) and a 05 May 2020, 06:18
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Point (2,0) (point on the circle) will be at the maximum distance from point (-5,0)
Therefore distance between points= 7 units
Option C

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What is the maximum possible distance between the point (-5, 0) and a 05 May 2020, 07:03
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rohitambasta
Point (2,0) (point on the circle) will be at the maximum distance from point (-5,0)
Therefore distance between points= 7 units
Option C

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Hi rohitambasta
Welcome to GMAT CLUB :)

Quote:
What is the maximum possible distance between the point (-5, 0) and a point on the circle x^2 + y^2 = 4 ?

A. 3
B. 5
C. 7
D. 8
E. 9
Show more

Please find the video solution as mentioned below. Drawing the figure is recommended for more beginners.

ANswer: Option C

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What is the maximum possible distance between the point (-5, 0) and a 09 May 2020, 06:21
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Bunuel
What is the maximum possible distance between the point (-5, 0) and a point on the circle x^2 + y^2 = 4 ?

A. 3
B. 5
C. 7
D. 8
E. 9
Show more

We see that (-5, 0) is on the x-axis, and the circle with equation x^2 + y^2 = 4 is a circle centered at the origin with radius 2. Thus, the circle also has two points on the axis: (-2, 0) and (2, 0). We see that (-2, 0) is the point on the circle that is closest to (-5, 0), and (2, 0) is the point on the circle that is farthest from (-5, 0). Therefore, the maximum possible distance between (-5, 0) and a point on the circle is |-5 - 2| = 7. (Note the minimum possible distance is |-5 - (-2)| = 3.)

Answer: C
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What is the maximum possible distance between the point (-5, 0) and a 09 May 2020, 07:07
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Answer is C.
Equation x^2+y^2 = 4, can have solution (2,0).
Now if we draw it on the number line, distance between (-5,0)-----(2,0) = 7
Since these are the farthest points to each other, the answer is 7.
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What is the maximum possible distance between the point (-5, 0) and a 16 Aug 2020, 09:58
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Solution: x^2 + y^2 = 4 is equation of circle with radius 2.

Distance between (-5,0) and (2,0) is maximum whcih is 7. please refer diagram for details.
Attachments

Circel.png
Circel.png [ 6.69 KiB | Viewed 8191 times ]

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What is the maximum possible distance between the point (-5, 0) and a 02 Sep 2020, 01:30
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ScottTargetTestPrep
Bunuel
What is the maximum possible distance between the point (-5, 0) and a point on the circle x^2 + y^2 = 4 ?

A. 3
B. 5
C. 7
D. 8
E. 9

We see that (-5, 0) is on the x-axis, and the circle with equation x^2 + y^2 = 4 is a circle centered at the origin with radius 2. Thus, the circle also has two points on the axis: (-2, 0) and (2, 0). We see that (-2, 0) is the point on the circle that is closest to (-5, 0), and (2, 0) is the point on the circle that is farthest from (-5, 0). Therefore, the maximum possible distance between (-5, 0) and a point on the circle is |-5 - 2| = 7. (Note the minimum possible distance is |-5 - (-2)| = 3.)

Answer: C
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ScottTargetTestPrep, how do I know that the circle is centered at the origin?
Is it because the (x2-x1)^2 + (y2-y1)^2 = r^2 formula has already been reduced by having two coordinates at zero?
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What is the maximum possible distance between the point (-5, 0) and a 18 Sep 2020, 07:22
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Bunuel
What is the maximum possible distance between the point (-5, 0) and a point on the circle x^2 + y^2 = 4 ?

A. 3
B. 5
C. 7
D. 8
E. 9

We see that (-5, 0) is on the x-axis, and the circle with equation x^2 + y^2 = 4 is a circle centered at the origin with radius 2. Thus, the circle also has two points on the axis: (-2, 0) and (2, 0). We see that (-2, 0) is the point on the circle that is closest to (-5, 0), and (2, 0) is the point on the circle that is farthest from (-5, 0). Therefore, the maximum possible distance between (-5, 0) and a point on the circle is |-5 - 2| = 7. (Note the minimum possible distance is |-5 - (-2)| = 3.)

Answer: C

ScottTargetTestPrep, how do I know that the circle is centered at the origin?
Is it because the (x2-x1)^2 + (y2-y1)^2 = r^2 formula has already been reduced by having two coordinates at zero?
Show more

The general formula for the circle with center at (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2. Now, rewrite the equation x^2 + y^2 = 4 as follows:

(x - 0)^2 + (y - 0)^2 = 2^2

Comparing the above to the general formula, we see that a = b = 0 and r = 2. Thus, the center is (a, b) = (0, 0) and the radius is 2.
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