The distance between the points (7,7) and (k,-5) 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 (7,7) and (k,-5) = 13

=> $$\sqrt{(-5-7)^2 + (k - 7)^2} = 13$$

=> $$144 + (k^2 - 14k + 49) = (13)^2 = 169$$

=> $$k^2 - 14k = 169 - 49 - 144$$

=> $$k^2 - 14k + 24 = 0$$

=> $$k^2 - 12k - 2k + 24 = 0$$

=> $$k(k - 12) - 2(k - 12) = 0$$

=> $$(k - 12) (k - 2) = 0$$

=> $$k = 12 , 2$$

=> Ans - (D)