Question 125671
let's first graph given parabola {{{y=x^2}}} and a line {{{y=2x-5}}}


{{{graph( 600, 400, -10, 10, -20, 20, x^2, 2x-5) }}}

as you can see, there are no points of intersection

on a graph above we have given parabola {{{y=x^2}}} and line {{{2x-5}}}

now, I will add a line {{{2x-1}}} parallel to the given line {{{2x-5}}}(these lines have same slopes) which will be a tangent (there will be one point of intersection) on parabola {{{x^2}}}; the distance between these two parallel lines will be equal to the distance between the given line and parabola


{{{graph( 600, 400, -10, 10, -20, 20, x^2, 2x-5, 2x-1) }}}


now, we can choose two points (one on each of parallel lines) and find a distance between them; it will be also equal to the distance between parabola and the given line


*[invoke hummingbird_distance_2D 0, -1, 0, -5]



answer is: the distance is {{{4}}}