Here is the graph of the equation I've managed to draw with Desmos.
##x=-{\frac 5 4}## is the solution I got but it lies outside the graph, but the minimum distance should be at ##(-1,0)##. At least according to the book.
Since ##x=-{\frac 5 4}## is outside the graph, I guess it won't have a y-coordinate.
Even from the equation of the graph, I get ##y=\sqrt{-{\frac 5 8}}##, which is invalid.
The Attempt at a Solution
I know the answer is supposed to be ##(-1,0)##.
However when I differentiate the above expression I get.
$$
2x+{\frac 5 2}
$$
Then the shortest distance would be when the expression equates to 0.
$$
2x+{\frac 5 2}=0
$$
I should be getting ##x=-1## but solving for ##x##...