Coordinate Geometry Ellipse

Please help me solve this (Doh)

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 ^^

Re: Coordinate Geometry Ellipse

i think its not the midpoint

Re: Coordinate Geometry Ellipse

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Re: Coordinate Geometry Ellipse

Re: Coordinate Geometry Ellipse

Re: Coordinate Geometry Ellipse

Quote:

Originally Posted by

**earboth** 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)

thank you sir for the answer !!! now I understand :)

Re: Coordinate Geometry Ellipse

Quote:

Originally Posted by

**mventurina1** thank you sir for the answer !!! now I understand :)

Hello,

I noticed to late that there is a second solution.

There exists a second directrix whose equation is

This directrix crosses the straight line a in

The midpoint between F and P is indeed C. So the statement in the question is true under certain conditions.

Re: Coordinate Geometry Ellipse

Quote:

Originally Posted by

**earboth** Hello,

I noticed to late that there is a second solution.

There exists a second directrix whose equation is

This directrix crosses the straight line a in

The midpoint between F and P is indeed C. So the statement in the question is true under certain conditions.

you mean under certain conditions . the focus is the midpoint of the directrix and center?

Re: Coordinate Geometry Ellipse

Quote:

Originally Posted by

**mventurina1** you mean under certain conditions . the focus is the midpoint of the directrix and center?

Hello,

please do me a favor and forget my last answer - it is wrong. I must have had a brain blackout. Sorry for the confusion!

Re: Coordinate Geometry Ellipse

Quote:

Originally Posted by

**earboth** Hello,

please do me a favor and forget my last answer - it is wrong. I must have had a brain blackout. Sorry for the confusion!

Sure and thanks again Sir !