i think its not the midpoint
Please help me solve this
Q: is the midpoint from directrix to C the focus?
determine the equation and graph of the ellipse w/ center at (4,-5), major axis vertical. eccentricity=√21/5 distance between directrices=50√21/21
(note: distance from C to a directrix = a/e or a^{2}/c) note (e = c / a)
Thanks in advance for the reply ^^
Good morning,
1. Let d denotes the distance from C to the directrix. Then you know
With follows:
2. Since
3. Therefore the equation of the ellipse is:
4. The coordinates of the foci are and
5. The equation of the upper directrix is
6. The major axis is placed on the straight line a (see attachment). d crosses a in the point
7. The midpoint between C and D is which is definitely not the focus F (compare the result at #4)