Prove that the focal distance of the point `(x ,y)` on the parabola `x^2-8x+16 y=0` is `|y+5|`

Explanation

`x^(2)-8x+16y=0`
`i.e., (x-4)^(2)=-16y+16`
i.e., ` (x-4)^(2)=-16(y-1)` (1)
Therefore, the focus is (4,-3).
The focul distance of any point on a parabola is its distance from the focus.
Therefore, the focal distance of P(x,y) on the parabola is
`sqrt((x-4)^(2)+(y+3)^(2))=sqrt(-16(y-1)+(y+3)^(2))`
`=sqrt((y+5)^(2))=|y+5|`