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
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
6 answers
that cant be, because you need to find the values for those number of values
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
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
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
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
@ GanonTEK i understand what you mean. i understand what to do now, thank you
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
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