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
