Chapter 10 - Parametric Equations and Polar Coordinates - 10.5 Exercises - Page 700: 35

$(y-3)=2(x-2)^2$

Distance of the point $(x,y)$ from the line $y=k$ is $|y-k|$ Therefore, the equation of the parabola is $|y-k|=\sqrt {(x-2)^2+(y-6+k)^{2}}$ Squaring both sides, $(y-k)^2=(x-2)^2+(y-6+k)^{2}$ .....(1) $(5-k)^2=1+(k-1)^2$ $k=\frac{23}{8}$ Put this value in equation (1) and we have $(y-3)=2(x-2)^2$