In the xy plane, point (r,s) lies on the circle with the cen

[mitzwillrockgmat]

In the xy plane, point (r,s) lies on the circle with the centre at the origin. What is the value of r^2 +s^2?

1. The circle has radius 2
2. The point (v2,-v2) lies on the circle v=square root

Help out with statement 2 please!

1. radius is 2, so i can use circle of eq formula x^2 +y^2= R^2 (radius)... so r^2 +s^2 =2^2 => 4

2. im a bit confused here - does it simply mean that we can substitute sqroot 2 & (-) sqroot 2 to get answer? so then, (sqroot2)^2 + [ - (sqroot 2)]^2 = r^2 +s^2 ? hence, the answer agn is 4

I'm thinking that this must be correct since answer is D.

By the way i could've also interpreted "on the circle" to mean that the points are inside the circle.
So, is it safe to say that "on the circle" ALWAYS means that the points are on the circumference & NOT, inside the circle?

[Rich@VeritasPrep]

Mitz,

Yes, you are correct.

If the point (sqrt(2), -sqrt(2)) is on the circle, that means that the x and y coordinates both have the same absolute value, which means that you could draw a 45-45-90 right triangle with the points (0,0), (sqrt(2), 0), and (sqrt(2), -sqrt(2)) as vertices.

The hypotenuse of this triangle, which has length 2, would also be the radius of the circle. r^2+s^2 is the square of the radius, and thus you can find r^2 + s^2.

Also, "on the circle" will always mean along the circumference. If the question means to specify a point inside the circle, it will state as exactly that or something similar, such as "within the circle".

[mitzwillrockgmat]

Mitz,

Yes, you are correct.

If the point (sqrt(2), -sqrt(2)) is on the circle, that means that the x and y coordinates both have the same absolute value, which means that you could draw a 45-45-90 right triangle with the points (0,0), (sqrt(2), 0), and (sqrt(2), -sqrt(2)) as vertices.

The hypotenuse of this triangle, which has length 2, would also be the radius of the circle. r^2+s^2 is the square of the radius, and thus you can find r^2 + s^2.

Also, "on the circle" will always mean along the circumference. If the question means to specify a point inside the circle, it will state as exactly that or something similar, such as "within the circle".

Cool! thanks Raz

[Scott@TargetTestPrep]

In the xy plane, point (r,s) lies on the circle with the centre at the origin. What is the value of r^2 +s^2?

1. The circle has radius 2
2. The point (v2,-v2) lies on the circle v=square root

Solution:

Question Stem Analysis:

We need to determine the value of r^2 + s^2, given that (r, s) is a point on the circle with center at the origin. Notice that the equation of such a circle is x^2 + y^2 = R^2 where R is the radius of the circle. Since (r, s) is a point on the circle, we have r^2 + s^2 = R^2. That is, in order to determine the value of r^2 + s^2, we either need to know the coordinates of a point on the circle or just the value of R.

Statement One Alone:

Since the radius of the circle is 2, R = 2. Therefore, r^2 + s^2 = 2^2 = 4. Statement one alone is sufficient.

Statement Two Alone:

Since (√2, -√2) is a point on the circle, x = √2 and y = -√2 will satisfy x^2 + y^2 = R^2. Substituting, we find R^2 = x^2 + y^2 = (√2)^2 + (-√2)^2 = 2+ 2 = 4. Proceeding as above, we obtain r^2 + s^2 = 4. Statement two alone is sufficient.

Answer: D