The distance between the points (11,­5) and (k,0) is 13. Find k.

Distance between two points $$(x_1 , y_1)$$ and $$(x_2 , y_2)$$ = $$\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$$

Now, distance between points (11,5) and (k,0) = 13

=> $$\sqrt{(0 - 5)^2 + (k - 11)^2} = 13$$

=> $$25 + (k^2 - 22k + 121) = (13)^2 = 169$$

=> $$k^2 - 22k = 169 - 25 - 121$$

=> $$k^2 - 22k - 23 = 0$$

=> $$k^2 + k - 23k - 23 = 0$$

=> $$k(k + 1) - 23(k + 1) = 0$$

=> $$(k + 1) (k - 23) = 0$$

=> $$k = -1 , 23$$