one vertex at (2,5) and one co-vertex at (−1,1). What is the standard and general forms of equation of the ellipse.

Question

The given are one vertex at (2,5) and one co-vertex at (−1,1). what is the standard and general form of the equation. Must have solution for this.

Answer 1

If you plot the 2 points and draw a vertical line thru (2,5) and a horizontal line thru (-1,1). you will find that they intersect at (2,1). This is your center.

The distance from the center to the vertex is 4. This gives a = 4

The distance from the center to the co-vertex is 3. This gives b = 3

The equation will be (y - 1)²/16 + (x - 2)²/9 = 1