How many points of intersection does the curve x² + y² = 4 have with line x + y = 2?
A) 0
B) 1
C) 2
D) 3
E) 4

The points of intersection will be points (x,y) that satisfy BOTH equations.

So, how many different solutions does this system have?
x² + y² = 4
x + y = 2

If x + y = 2 then x = 2 - y
Now take x² + y² = 4 and replace x with (2 - y) to get: (2 - y)² + y² = 4
Expand: 4 - 4y + y² + y² = 4
Simplify: 2y² - 4y = 0
Factor: 2y(y - 2) = 0
Solve: y = 0 or y = 2

If y = 0 (and x + y = 2), then x = 2. So, one point of intersection is (2, 0)
If y = 2 (and x + y = 2), then x = 0. So, another point of intersection is (0, 2)

So, we have 2 points of intersection in total.
Answer: C

Cheers,
Brent

Hi shibsriz,

If you want to do the work, the two equations in this question can be physically graphed, so that you can "see" the points of intersection.

You don't need to graph it, but you have to recognize the rarer graphing rule in this question:

The equation X^2 + Y^2 = 4 is a circle, centered around the Origin, with a radius of 2. The points (2,0), (0,2), (-2,0) and (0,-2) are all on the circumference of the circle

The equation X + Y = 2 can be rewritten as Y = -X + 2 and will be a straight line.

By definition, the line will intersect with the circle at either 0, 1 or 2 points.

Knowing the above 4 "obvious" points on the circle will allow you to quickly find 2 points on the line: (2,0) and (0,2). Then you can stop; a line can't intercept a circle at more than 2 points.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich