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# In the xy-plane the point (-2 -3) is the centre of a circle, the point

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Joined: 18 Feb 2015
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In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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Updated on: 16 Dec 2015, 15:18
9
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:51) correct 24% (02:28) wrong based on 246 sessions

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In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then r=

A) 6
B) 5
C) 4
D) 3
E) 2

Originally posted by HarveyKlaus on 16 Dec 2015, 13:51.
Last edited by ENGRTOMBA2018 on 16 Dec 2015, 15:18, edited 1 time in total.
Formatted the question
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Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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16 Dec 2015, 22:57
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2
HarveyKlaus wrote:
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then r=

A) 6
B) 5
C) 4
D) 3
E) 2

In co-ordinate geometry, you should always draw the figure to get the relative placement of points.
Attachment:

Ques3.jpg [ 1.3 MiB | Viewed 3756 times ]

When you draw it, you will see that (-2, 1) is 4 away from the centre and (4, -3) is 6 away from the centre. So the radius of the circle must be between 4 and 6. The only possible value is 5.
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Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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16 Dec 2015, 15:16
Ans B. Here is how I solved it.

Given that the center of the circle is at (-2,-3) and radius = r (r is an integer). Also given that the point (-2,1) lies inside this circle and (4,-3) lies outside this circle.

With this info, lets draw a circle with center at (-2,-3) and passing through the point (-2,1) and lets call the radius of this (smaller) circle Rs such that Rs<r.

We can calculate the radius of the smaller circle Rs (as we have its center and a point on the smaller circle). Calculation below:

$$Rs^2$$ = $$(-2+2)^2$$ + $$(-3-1)^2$$. This will give us the value of Rs = 4 units.

Similarly, we can also draw another circle with center (-2,-3) and passing through (4,-3). Let the radius of this bigger circle be Rb such that Rb>r>Rs.

We can calculate Rb (as we have its center and a point on the larger circle). Calculation below:

$$Rb^2$$ = $$(-2-4)^2$$ + $$(-3+3)^2$$. This will give us the value of Rb = 6 units.

Now we have 3 concentric circles with the radii in the order : Rb>r>Rs or 6>r>4.

The only integer value to satisfy the above equation is r=5.

Hope it helps?
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Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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16 Dec 2015, 15:36
2
HarveyKlaus wrote:
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then r=

A) 6
B) 5
C) 4
D) 3
E) 2

Can be solved without much calculations.

You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,1) ----> greater than 4 units.

Thus the radius is >4 but <6 and as it is an integer, the only possible value of radius = 5 units.

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Joined: 19 Oct 2015
Posts: 28
Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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14 Jul 2017, 07:57
(-2,-3) Origin of the circle
(-2,1) lies inside circle and lies in IInd quadrant
(4,-3) lies outside circle and lies in IV quadrant

To take on this question is good to consider range
First calculate the distance between each points

From Above
Points inside circle are separated from each other with distance of 4 - Calculate from distance formula
points outside circle is separated from origin with distance of 6

So your boundary values are (4---6)
So the circle's radius lies between (4--6)
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Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point  [#permalink]

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08 Aug 2018, 23:44
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Re: In the xy-plane the point (-2 -3) is the centre of a circle, the point &nbs [#permalink] 08 Aug 2018, 23:44
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