# The point C has coordinates (2,k) and the distance from A to C is 5. Find the 2 possible values of the constant k

The coordinates of A are (6, -2) I have managed to do every other question in this section but this one, my brother tried to help but just drew a graph and the answers without explaining it, i dont understand the technique behind it? thanks for your help

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Are you familiar with the distance formula? –  flodyninja Sep 18 '12 at 19:01
square root around (y1-y2)squared + (x1-x2)squared..? then yes but you end up with a k squared minus a k –  Jamie Hawk Sep 18 '12 at 19:03

Hint: By the Distance Formula, or equivalently by the Pythagorean Theorem, $$\sqrt{(2-6)^2+(k-(-2))^2}=5.$$ Square both sides and simplify. You will get a quadratic equation in $k$. Solve. To solve, you can use the Quadratic Formula, or note that the resulting quadratic factors nicely.
I get, after simplifying, the equation $k^2+4k-5=0$. –  André Nicolas Sep 18 '12 at 19:08