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A circle in the XY-plane has its center at the origin. If M is a point 06 Nov 2018, 01:44
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A circle in the XY-plane has its center at the origin. If M is a point on the circle, what is the sum of the squares of the coordinates of M?

(1) The radius of the circle is 5.
(2) The sum of the coordinates of M is 7.
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A circle in the XY-plane has its center at the origin. If M is a point Updated on: 06 Nov 2018, 19:24
Originally posted by eswarchethu135 on 06 Nov 2018, 02:21.
Last edited by eswarchethu135 on 06 Nov 2018, 19:24, edited 1 time in total.
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Statement 1) The distance between two points is 5. One point is (0,0). No matter what the other point is distance from (0,0) will be x^2+y^2=25. Sufficient.

Statement 2) insufficient

OPTION: A
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A circle in the XY-plane has its center at the origin. If M is a point 06 Nov 2018, 04:09
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Bunuel
A circle in the XY-plane has its center at the origin. If M is a point on the circle, what is the sum of the squares of the coordinates of M?

(1) The radius of the circle is 5.
(2) The sum of the coordinates of M is 7.
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If we assume the point as (x,y) then the sum of the squares of coordinates is x^2+y^2 .
stat 1 : radius is 5 . That is sqrt[x^2+y^2] = 5 .=> x^2+y^2=25
sufficient .
stat2 : not sufficient
So ans is A .
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A circle in the XY-plane has its center at the origin. If M is a point 17 Jan 2021, 12:28
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Bunuel
A circle in the XY-plane has its center at the origin. If M is a point on the circle, what is the sum of the squares of the coordinates of M?

(1) The radius of the circle is 5.
(2) The sum of the coordinates of M is 7.
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Solution:

Since the circle is centered at the origin, if it has a radius of r, then an equation of the circle is x^2 + y^2 = r^2. Since M is a point on the circle, if M has the coordinates of (a, b), then a^2 + b^2 = r^2.

We need to determine the value of a^2 + b^2. We can see that if we know the value of r, then we can determine the value of a^2 + b^2 since it’s equal to r^2.

Statement One Only:

The radius of the circle is 5.

This means r = 5. Since r = 5, we see that a^2 + b^2 = 5^2 = 25. Statement one alone is sufficient.

Statement Two Only:

The sum of the coordinates of M is 7.

This means a + b = 7. If a = 3 and b = 4, a^2 + b^2 = 9 + 16 = 25. However, if a = 2 and b = 5, a^2 + b^2 = 4 + 25 = 29. Statement two alone is not sufficient.

Answer: A
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A circle in the XY-plane has its center at the origin. If M is a point 17 Sep 2022, 08:12
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