Question 1184801
{{{9y = x^2}}}

{{{y = (1/9)x^2}}}

the point of the parabola closest to the point ({{{5}}},{{{-2}}})

simply, that will be intersection point of the parabola {{{y = (1/9)x^2}}} and vertical line {{{x=5}}} that passes through the point ({{{5}}},{{{-2}}})

{{{y = (1/9)5^2}}}

{{{y = 25/9}}}

=> ({{{5}}},{{{25/9}}}) is the closest to the point ({{{5}}},{{{-2}}})



{{{ drawing( 600, 600, -10, 10, -10, 10, 
circle(5,-2,.12), locate(5,-2,p(5,-2)), circle(5,25/9,.12), locate(5,25/9,p(5,25/9)), green(line(5,7,5,-7)),
graph( 600, 600, -10, 10, -10, 10,  x^2/9)) }}}