I've attached a sketch of the ellips and the line.
Consider the distance between (0, 3) and (4, 0) to be the base of the triangle you are looking for. The base has a length of 5. Thus you need the height of the triangle so that the area is 3:
Therefore you need a parallel to the given line with the distance of . Calculate the coordinates of a point on the y-axis which has a distance of from the given line:
Use the distance formula:
Only is a valid value (otherwise the line will not intersect with the ellipse)
The parallel to the given line has the equation:
To get the coordinates of the points R and V calculate the intersection points of the ellipse and the parallel:
Plug in these x-values into the equation of the parallel to get the y-coordinates of the points R and V.