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A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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03 May 2016, 06:59
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A certain circle in the xyplane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P? 1) The radius of the circle is 4. 2) The sum of the coordinates of P is 0.
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Re: A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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03 May 2016, 07:01
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Could someone please elaborate what the term "sum of the squares" mean in the context of coordinate geometry?



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A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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03 May 2016, 08:40
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Hi Sallyzodiac, The centerradius form of the circle equation is in the format \((x – h)^2\) + \((y – k)^2\) = \(r^2\), with the center being at the point (h, k) and the radius being "r". Now if we are told that the circle lies on the origin, this equation is reduced to \(x^2 + y^2 = r ^2\). So, for us to calculate the squares of the coordinates  we just need to know the radius of the circle. Hence A.
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Re: A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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03 May 2016, 08:42
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Sallyzodiac wrote: A certain circle in the xyplane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P?
1) The radius of the circle is 4.
2) The sum of the coordinates of P is 0. Say the coordinates of P are (x,y), then the question asks about the value of x^2 + y^2. In an xy Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\) This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a rightangled triangle whose other sides are of length xa and yb. If the circle is centered at the origin (0, 0), then the equation simplifies to: \(x^2+y^2=r^2\). According to the above, the first statement of the question gives the direct answer: x^2 + y^2 = r^2 = 4^2. The second statement is not sufficient. Check more here: mathcoordinategeometry87652.htmlHope it helps.
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Re: A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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19 Jun 2016, 08:41
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Hi Bunuel  My confusion is on the wording of the question " If p is a point on the circle..." this is in fact saying that p has to be on the "outlined" circle and NOT for example inside the circle? If we choose p to be in the origin, 0,0 we would have another answer. But from what I am reading no one is considering P to be "inside" the circle. Are there any key clue to rule out points inside the circle? best Oloman Bunuel wrote: Sallyzodiac wrote: A certain circle in the xyplane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P?
1) The radius of the circle is 4.
2) The sum of the coordinates of P is 0. Say the coordinates of P are (x,y), then the question asks about the value of x^2 + y^2. In an xy Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\) This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a rightangled triangle whose other sides are of length xa and yb. If the circle is centered at the origin (0, 0), then the equation simplifies to: \(x^2+y^2=r^2\). According to the above, the first statement of the question gives the direct answer: x^2 + y^2 = r^2 = 4^2. The second statement is not sufficient. Check more here: mathcoordinategeometry87652.htmlHope it helps.



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Re: A certain circle in the xyplane has its center at the origin. If P is [#permalink]
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19 Jun 2016, 08:50
oloman wrote: Hi Bunuel  My confusion is on the wording of the question " If p is a point on the circle..." this is in fact saying that p has to be on the "outlined" circle and NOT for example inside the circle? If we choose p to be in the origin, 0,0 we would have another answer. But from what I am reading no one is considering P to be "inside" the circle. Are there any key clue to rule out points inside the circle? best Oloman Bunuel wrote: Sallyzodiac wrote: A certain circle in the xyplane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P?
1) The radius of the circle is 4.
2) The sum of the coordinates of P is 0. Say the coordinates of P are (x,y), then the question asks about the value of x^2 + y^2. In an xy Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\) This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a rightangled triangle whose other sides are of length xa and yb. If the circle is centered at the origin (0, 0), then the equation simplifies to: \(x^2+y^2=r^2\). According to the above, the first statement of the question gives the direct answer: x^2 + y^2 = r^2 = 4^2. The second statement is not sufficient. Check more here: mathcoordinategeometry87652.htmlHope it helps. Yes, on the circle means on the circumference, while in the circle means inside the circumference.
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Re: A certain circle in the xyplane has its center at the origin [#permalink]
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27 Aug 2016, 15:17
Question asked here is, nothing the square of the radius of the circle, since the circle is centered at origin. Statement that helps in finding out the radius of the circle is sufficient.
Hence A.



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Re: A certain circle in the xyplane has its center at the origin [#permalink]
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27 Aug 2016, 23:10
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Keats wrote: A certain circle in the xyplane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P?
(1)The radius of the circle is 4. (2)The sum of the coordinates of P is 0. We are given the center at origin, so equation of circle will be \(x^2 + y^2 = r^2\) Since, P is on the circle, it will satisfy this equation. Statement 1 : We are given the value of r = 4, so we can find out the value of \(x^2 + y^2\), Hence Sufficient. Statement 2 says x = y. Even if we put this value in the equation we will get \(2x^2 = r^2\) But Since we don't know r, we cannot find the value of x. hence, insufficient. Answer A.
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