Answer
$${\text{point}}$$
Work Step by Step
$$\eqalign{
& 4{x^2} - 24x + 5{y^2} + 10y + 41 = 0 \cr
& {\text{Subtract 41 from both sides}} \cr
& 4{x^2} - 24x + 5{y^2} + 10y = - 41 \cr
& {\text{Factor}} \cr
& 4\left( {{x^2} - 6x} \right) + 5\left( {{y^2} + 2y} \right) = - 41 \cr
& {\text{Complete the square and factor}} \cr
& 4\left( {{x^2} - 6x + 9} \right) + 5\left( {{y^2} + 2y + 1} \right) = - 41 + 4\left( 9 \right) + 5\left( 1 \right) \cr
& 4{\left( {x - 3} \right)^2} + 5{\left( {y + 1} \right)^2} = 0 \cr
& {\text{The equation is written in the form }}a{\left( {x - h} \right)^2} + b{\left( {y - k} \right)^2} = {r^2} \cr
& {\text{Beacuse }}r = 0 \cr
& {\text{The graph of the equation}}4{\left( {x - 3} \right)^2} + 5{\left( {y + 1} \right)^2} = 0{\text{ is a point}} \cr
& {\text{centered at }}\left( {3, - 1} \right) \cr} $$
