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Circle O is plotted on the coordinate plane. If point A, which is loca

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Circle O is plotted on the coordinate plane. If point A, which is loca  [#permalink]

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New post 20 Oct 2018, 09:24
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Circle O is plotted on the coordinate plane. If point A, which is located at (—3, y), and point B, which is located at (x, 4) are on the circumference of the circle, what is the value of y-x?
1) The center of circle O is at the origin of the coordinate plane.
2) x+y = 1

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Re: Circle O is plotted on the coordinate plane. If point A, which is loca  [#permalink]

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New post 20 Oct 2018, 09:33
E.

There are can be multiple values of y and x for them to be on the circumference of the circle.
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Re: Circle O is plotted on the coordinate plane. If point A, which is loca  [#permalink]

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New post 20 Oct 2018, 09:34
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Circle O is plotted on the coordinate plane. If point A, which is located at (—3, y), and point B, which is located at (x, 4) are on the circumference of the circle, what is the value of y-x?
1) The center of circle O is at the origin of the coordinate plane.
2) x+y = 1

Since origin is centre of circle x=0, y= 0

Point A distance from centre = square root (9+y^2)
Point B distance fro centre square root (x^2+16)

and they need to be equal as radius
so 9+y^2=16+x^2
hence (x-y)(x+y)=-7
now anything is possible any value of x-y is possible -1, or -7, or -3.5
hence not sufficient

Option B, x+y=1...which can meet A at (-3,4 ) and B at (4,-3) and both a and B will be the same hence not sufficient

Combining
x-y=-7 and hence y-x=7

hence C is the answer
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Re: Circle O is plotted on the coordinate plane. If point A, which is loca  [#permalink]

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New post 21 Oct 2018, 01:50
Stat 1) Since centre in at (0,0) and points A & B are on circumference then OA=OB= Radius
Using distance formula we get \(\sqrt{(-3-0)^2 + (y+0)2} = \sqrt{(x-0)^2 + (4-0)^2}\)
This simplifies t0 => \(y^2 - x^2 = 7\) => \((y+x) (y-x) = 7\) => so either y+x=7 & y-x =1 OR y+x= 1 & y-x=7.
two solution hence Insuff

Stat 2) itself is insuff

Both, we get y+x = 1 then y-x must be = 7 hence C
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Re: Circle O is plotted on the coordinate plane. If point A, which is loca   [#permalink] 21 Oct 2018, 01:50
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