SOLUTION: For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly two points?

Question 1056901: For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly two points?
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly two points?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 = 4,      (1)
y = kx + 4.       (2)

Substitute the expression y = kx + 4 from (2) into equation (1). You will get

 = 4.

Simplify

 = 4,

 = 0.

In order for the last equation has two different real roots, the discriminant must be positive:

d = b^2 - 4ac = (8k)^2 - 4*(1+k^2)*12 > 0,  or

    64k^2 - 48k^2 - 48 > 0,   or

    16k^2 > 48,   or

    k^2 > 3,   or

    k <   OR  k > .

Answer. The solution set is (,) U (,).

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