Question

For what values of k does the line y= x + k pass through the circle defined by x^2 + y^2 = 25 at:
2 points?
1 point?
0 points?
I found the discriminant: 100- 4k^2 but i don't know how to find for each of the points

Answer 1

your discriminant is correct

so for 2 points:
100-4k^2 > 0
-4k^2 > -100
k^2 < 25
-5 ≤ k ≤ +5

for 1 point
k = ± 5

for 0 points,
100 - 4k^2 < 0
k < -5 OR k > 5