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Is the intersection of two lines x + y = 8 and 4y - 4x=16 in

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Is the intersection of two lines x + y = 8 and 4y - 4x=16 in [#permalink] New post 17 Feb 2013, 19:55
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Is the intersection of two lines x + y = 8 and 4y - 4x=16 inside the circle: x^2 + y^2 = r^2

(1) r = 81
(2) The center of the circle is at the coordinate (-99,-99)

I doubt on OA , plz explain if you've got the right answer.
[Reveal] Spoiler: OA

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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 17 Feb 2013, 20:48
daviesj wrote:
Is the intersection of two lines x + y = 8 and 4y - 4x=16 inside the circle: x^2 + y^2 = r^2

1. r = 81

2. The center of the circle is at the coordinate (-99,-99)

I doubt on OA , plz explain if you've got the right answer.


We ahve two known lines and hence we can find the point of intersection. We need to find whether that point of intersection falls within a circle with centre at the origin and radius "r".

1) Radius can be found and hence circle can be plotted and whether the point falls within the circle or not can be determined. Sufficient.

2) I doubt this statement as it is contradictory to both the question statement and statement 1.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 05 Mar 2013, 17:39
If we know the radius and center , then we can determine whether a point lies in the circle or not.

By question statement it seems that center is at 0,0 if x and y are actual coordinates not the shifted ones

Option A tells us about radius , so it is sufficient.

Option B changes the question statement by shifting the coordinates 99 down and left and tells nothing about radius - so not sufficient.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 31 Jul 2013, 22:46
MacFauz wrote:
daviesj wrote:
Is the intersection of two lines x + y = 8 and 4y - 4x=16 inside the circle: x^2 + y^2 = r^2

1. r = 81

2. The center of the circle is at the coordinate (-99,-99)

I doubt on OA , plz explain if you've got the right answer.


We ahve two known lines and hence we can find the point of intersection. We need to find whether that point of intersection falls within a circle with centre at the origin and radius "r".

1) Radius can be found and hence circle can be plotted and whether the point falls within the circle or not can be determined. Sufficient.

2) I doubt this statement as it is contradictory to both the question statement and statement 1.


Please can body elaborate more on this? How can we find the point of intersection if equation of two lines are given?
Thanks.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 31 Jul 2013, 22:51
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stne wrote:

Please can body elaborate more on this? How can we find the point of intersection if equation of two lines are given?
Thanks.


To find the intersection of two lines, you have to solve the system of equations:

x + y = 8
4y - 4x=16

Personally I would multiply the first by 4 => 4x + 4y = 8*4 and sum it to the second => 4x + 4y +4y-4x=16+ 8*4 or 8y=48, y=6.
Now substitute the value of y into one of the two equations (does not matter which one) => x + 6 = 8 , x=2.
Point of intersection (2,6).

Hope it's clear.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 31 Jul 2013, 22:58
Zarrolou wrote:
stne wrote:

Please can body elaborate more on this? How can we find the point of intersection if equation of two lines are given?
Thanks.


To find the intersection of two lines, you have to solve the system of equations:

x + y = 8
4y - 4x=16

Personally I would multiply the first by 4 => 4x + 4y = 8*4 and sum it to the second => 4x + 4y +4y-4x=16+ 8*4 or 8y=48, y=6.
Now substitute the value of y into one of the two equations (does not matter which one) => x + 6 = 8 , x=2.
Point of intersection (2,6).


Hope it's clear.



Great that helps +1 ! Also the equation of the circle x^2+ y^2 =r^2 , does this equation mean that the circle is centered at the origin, passes through xand y and has a radius r?
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 31 Jul 2013, 23:03
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stne wrote:

Great that helps +1 ! Also the equation of the circle x^2+ y^2 =r^2 , does this equation mean that the circle is centered at the origin, passes through xand y and has a radius r?


Yes.
The equation of a circle is (x-a)^2+(y-b)^2=r^2, where the point (a,b) is the center, and here is (0,0); and r is the radius.

The circle passes through the point (x,y) that satisfy that equation.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 28 Dec 2013, 16:15
Zarrolou wrote:
stne wrote:

Great that helps +1 ! Also the equation of the circle x^2+ y^2 =r^2 , does this equation mean that the circle is centered at the origin, passes through xand y and has a radius r?


Yes.
The equation of a circle is (x-a)^2+(y-b)^2=r^2, where the point (a,b) is the center, and here is (0,0); and r is the radius.

The circle passes through the point (x,y) that satisfy that equation.


But I don't get it how come question stem says circle is centered at original whilst second statement states other coordinates for the center of the circle?

Would anybody clarify if the question is indeed flawed as I suspect it is?

Cheers!
J :)
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16 [#permalink] New post 28 Dec 2013, 21:41
jlgdr wrote:
Zarrolou wrote:
stne wrote:

Great that helps +1 ! Also the equation of the circle x^2+ y^2 =r^2 , does this equation mean that the circle is centered at the origin, passes through xand y and has a radius r?


Yes.
The equation of a circle is (x-a)^2+(y-b)^2=r^2, where the point (a,b) is the center, and here is (0,0); and r is the radius.

The circle passes through the point (x,y) that satisfy that equation.


But I don't get it how come question stem says circle is centered at original whilst second statement states other coordinates for the center of the circle?

Would anybody clarify if the question is indeed flawed as I suspect it is?

Cheers!
J :)


yes the equation of the circle in general form is (x-a)^2+(y-b)^2=r^2 where a and b are the coordinates of the center, but over here it is given that the equation of the circle is x^2+ y^2 =r^2 hence a and b are 0, so the circle is centered at the origin. This is in contradiction with statement 2.

Yes you are correct, the statement 2 contradicts with the stem.

Also mentioned here : is-the-intersection-of-two-lines-x-y-8-and-4y-4x-147421.html#p1183570

hope that helps.
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Re: is the intersection of two lines x + y = 8 and 4y - 4x=16   [#permalink] 28 Dec 2013, 21:41
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