Question

For what values of k does the line y= x + k pass through the circle defined by x^2 + y^2 = 25 at:
a) 2 points
b) 1 point
c) 0 points

Answer 1

sub in y = x+k
x^2 + y^2 = 25
x^2 + (x+k)^2 = 25
x^2 + x^2 + 2kx + k^2 - 25 = 0
2x^2 + 2kx + (k^2-25) = 0
a = 2, b = 2k, c = k^2-25
discriminant = b^2 - 4ac
= 4k^2 - 4(2)(k^2-25)
= 4k^2 - 8k^2 + 100
= 100 - 4k^2

now proceed the same way as in the previous post to "Eloise"

Answer 2

I believe your last few lines are incorrect:

What was written:
4k^2 - 4(2)(k^2-25)
= 4k^2 - 8k^2 + 100
= 100 - 4k^2

What it should read:
4k^2 - 4(2)(k^2-25)
= 4k^2 - 8k^2 + 200
= 200 - 4k^2