Question

What will be the coordinates of focus of translated parabola
$x^2-2x=4y-5$

Answer 1

Given, equation of translated parabola as $x^2-2x=4y-5.$
On rearranging the equation we get,
$\Rightarrow x^2-2x+1=4y-4$
$\Rightarrow (x-1{)}^2=4(y-1)$
Vertex of this parabola is $(1,1)$ and $a=1.$
So, the coordinates of focus is $(h,k+a)$ i.e $(1,2).$