Find all points having an x-coordinate of 14 whose distance from the point (9,7) is 13

Question

Find all points having an x-coordinate of 14 whose distance from the point (9,7) is 13

Answer 1

(14,y) is 13 from (9,7)

13^2 = 169 = (y-7)^2 + 5^2

y^2 -14y +49 +25 = 169

y^2 -7y -85=0

y = 7/2 + (1/2)sqr(49+4(85)) = (7+/-sqr389)/2

= about 26.72/2 =13.36 or -12.72/2=-6.36

two points are about (14, 13) and (14,-6)