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# If the equation |x| + |y| = 5 encloses a certain region on

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Director
Joined: 09 Aug 2006
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If the equation |x| + |y| = 5 encloses a certain region on [#permalink]  20 Nov 2007, 21:09
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If the equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?

Can someone please explain to me why the region is a square and not a circle? Isn't x^2 + y^2 = A an equation of a circle? Thanks.
CEO
Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Expert's post
one has 4 cases:

1. x>0,y>0 ==> x+y=5 ==> (0,0), (5,0), (0,5) triangle with S1=25/2
2. x<0,y>0 ==> -x+y=5 ==> (0,0), (-5,0), (0,5) triangle with S2=25/2
3. x>0,y<0 ==> x-y=5 ==> (0,0), (5,0), (0,-5) triangle with S3=25/2
4. x<0,y<0 ==> -x+y=5 ==> (0,0), (-5,0), (0,-5) triangle with S4=25/2

S=4*25/2=50
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Director
Joined: 09 Aug 2006
Posts: 763
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Kudos [?]: 76 [0], given: 0

walker wrote:
one has 4 cases:

1. x>0,y>0 ==> x+y=5 ==> (0,0), (5,0), (0,5) triangle with S1=25/2
2. x<0>0 ==> -x+y=5 ==> (0,0), (-5,0), (0,5) triangle with S2=25/2
3. x>0,y<0> x-y=5 ==> (0,0), (5,0), (0,-5) triangle with S3=25/2
4. x<0,y<0> -x+y=5 ==> (0,0), (-5,0), (0,-5) triangle with S4=25/2

S=4*25/2=50

|x| + |y| = 5 or x^2 + y^2 = 5
Why can't this equation represent the area of a circle with radius 5?
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2244 [0], given: 359

Expert's post
1. x>0,y>0 ==> x+y=5 (y=x-5) - it is line (y=kx+b), it is not a circle.

x^2 + y^2 = 5 has radius root(5) you mean 25.

you can take a few (x,y) and put in both equations.
for example,
(5,0):
x+y=5 ok
x^2+y^2=25 ok

but for (4,1):
x+y=5 ok
x^2+y^2=17<25 (does not satisfy)
GMAT Instructor
Joined: 04 Jul 2006
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GK_Gmat wrote:
walker wrote:
one has 4 cases:

1. x>0,y>0 ==> x+y=5 ==> (0,0), (5,0), (0,5) triangle with S1=25/2
2. x<0>0 ==> -x+y=5 ==> (0,0), (-5,0), (0,5) triangle with S2=25/2
3. x>0,y<0> x-y=5 ==> (0,0), (5,0), (0,-5) triangle with S3=25/2
4. x<0,y<0> -x+y=5 ==> (0,0), (-5,0), (0,-5) triangle with S4=25/2

S=4*25/2=50

|x| + |y| = 5 or x^2 + y^2 = 5
Why can't this equation represent the area of a circle with radius 5?

When we square both sides, we get
x^2 +2|xy| + y^2 =25, which is not the equation of a circle with radius 5
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