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A certain circle in the xy-plane has its center at the 07 Nov 2008, 14:02
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A certain circle in the xy-plane has its center at the origin. If P is a mid point of the arc on the I quadrant, what are the coordinates of P? Radius of the circle is 4.

Please, explain your answer. This is a reworded problem from GMAT Set 31, therefore I have no OA for it.



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A certain circle in the xy-plane has its center at the 07 Nov 2008, 14:25
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It must be (2sqrt(2),2sqrt(2)).

Since it is mid point of the arc, both the values for X and Y must be same and diagonal is 4. So, if we take side as x

2x^2=16
x^2=8
x=sqrt(8)
x=2sqrt(2)

Since x=y we get (2sqrt(2),2sqrt(2)).
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A certain circle in the xy-plane has its center at the 07 Nov 2008, 14:52
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vikram, thanks for an answer.

what additional info would you need to calculate the coordinate of P, if P is an arbitrary point in the circle?
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A certain circle in the xy-plane has its center at the 07 Nov 2008, 15:02
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botirvoy
vikram, thanks for an answer.

what additional info would you need to calculate the coordinate of P, if P is an arbitrary point in the circle?
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Since it is a circle, value of one of the attributes or the angle between point and one of the axis should be the other attributes we can use to determine the values.
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A certain circle in the xy-plane has its center at the 07 Nov 2008, 16:41
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vishy007
botirvoy
vikram, thanks for an answer.

what additional info would you need to calculate the coordinate of P, if P is an arbitrary point in the circle?


Since it is a circle, value of one of the attributes or the angle between point and one of the axis should be the other attributes we can use to determine the values.
Show more
How should we deal, say, if such angle is 25 degrees? Again, thank you for taking time!
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A certain circle in the xy-plane has its center at the 07 Nov 2008, 18:55
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vishy007
It must be (2sqrt(2),2sqrt(2)).

Since it is mid point of the arc, both the values for X and Y must be same and diagonal is 4. So, if we take side as x

2x^2=16
x^2=8
x=sqrt(8)
x=2sqrt(2)

Since x=y we get (2sqrt(2),2sqrt(2)).
Show more


I guess you meant radius when you said diagonal.

Also, can you elaborate on this?

Since it is mid point of the arc, both the values for X and Y must be same
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A certain circle in the xy-plane has its center at the 10 Nov 2008, 09:26
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icandy
vishy007
It must be (2sqrt(2),2sqrt(2)).

Since it is mid point of the arc, both the values for X and Y must be same and diagonal is 4. So, if we take side as x

2x^2=16
x^2=8
x=sqrt(8)
x=2sqrt(2)

Since x=y we get (2sqrt(2),2sqrt(2)).


I guess you meant radius when you said diagonal.

Also, can you elaborate on this?

Since it is mid point of the arc, both the values for X and Y must be same
Show more


icandy,

I meant "diagonal" when I stated diagonal. However, the diagonal and radius here are the same. Let me explain.
Since it is mid point of the arc, both the values for X and Y must be same

We are dealing here with an arc (1/4 of the circle) within one quadrant. Mid point in the arc must be one where the line joining mid point and origin will make 45 degrees from both x axis and y axis. Now imagine that you are drawing a rectangle making the line joining origin and mid point of arc as diagonal. Now you can see that the rectangle satisfying this criteria will be a square. You can easily find out the lengths from there on.
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