Find a point on the ellipse x ^ 2 + 4Y ^ 2 = 4 to make it the shortest distance to the plane 2x + 3y-6 = 0

Find a point on the ellipse x ^ 2 + 4Y ^ 2 = 4 to make it the shortest distance to the plane 2x + 3y-6 = 0

Thinking:
1. Let a straight line be ax + by + C = 0 (the slope of this straight line is the same as that of the straight line in the title, because only if the slope is the same, the straight lines will be parallel, and then talk about the problem of distance. Two non parallel lines have no distance.)
2. By combining ax + by + C = 0 and elliptic equation, the discriminant of quadratic function is obtained, i.e. △ = 0 (tangent between straight line and ellipse), and C is obtained. In this way, the distance between two straight lines, the maximum distance and the minimum distance can be obtained
Supplement: in general, in conic curve to find the maximum distance or minimum distance of a straight line, the method is what I said above, to set a straight line parallel to a known straight line, and then use the tangent line and graph to find the unknown