Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0)
First, we express y as a function of x using the equation of ellipse:
This means that the distance from point (1,0) depends only on x coordinate of ellipse.
Notice that the distance squared function is parabola that opens downwards, so its maximum value occurs at vertex.
x−coordinate of vertex is:
We have x coordinate of point that is farthest to (1,0). Find y coordinate