If the point P on the curve,$4x^2+5y^2=20$  is farthest from the point Q(0, -4),then${\left(PQ\right)}^2=$

The point Q(0, -4 )lies on $y-$ axis.  farthest point on the ellipse must be end points of either major  axis or minor axis

The distance between the point Q(0, -4) and the ends of the major axis is 3 units only

The square of the distance between the point Q(0, -4)  and one end of the minor axis P(0,2) is  ${\left(PQ\right)}^2=36$