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, and 0 points
i found the discriminant which is 100 - 4k^2
but im not sure how to find the values for each point

Answer 1

if 100 - 4k^2 > 0 then you get 2 points
if 100 - 4k^2 = 0 then you get 1 point
if 100 - 4k^2 < 0 then you get 0 points

Answer 2

that cant be, because you need to find the values for those number of values

Answer 3

if the discriminant is zero, there is only one root, hence only one point of intersection.

positive, two roots
negative zero roots

Incidentally, you'd better check your discriminant. If you graph y=x+5, you will see that it intersects in two points, not 1.

http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%3D25%2C+y%3Dx%2B5

Answer 4

No, no it asks you for the values of k that let you get 2pts or 1pt or 0pts.

You have to solve each of those.

E.g.
100 - 4k^2 = 0
100 = 4k^2
25 = k^2
5 = k

So, when k = 5 you get only 1 point

100 - 4k^2 > 0
100 > 4k^2
25 > k^2
5 > k

So, when k > 5 you get 2 points

etc

Answer 5

@ GanonTEK i understand what you mean. i understand what to do now, thank you

Answer 6

You're welcome Jackie. Steve is right about the discriminant being incorrect by the way.

x^2 + y^2 = 25
y = x - k
x^2 + x^2 - 2xk +k^2 = 25
2x^2 - 2xk + k^2 - 25 = 0

x = 2k +- Sqrt(4k^2 - 4(2)(k^2 - 25)))/4

your discriminant is

-4k^2 + 200