Determine eqn of conic, given F(3,1), directrix x-1=>0, ecc.

[Aladdin]

I'm taking summer lessons next year preperations. I started a new topic(lesson) called Conics.
As I know every beginning has a start .

The question ::

Determine the equation of the conic C(F,d,e).Determine the nature of C(F,d,e) and its different elements.
Given:
F(3,1)
Equation of directrix : x-1= >0
Eccentricity :

My work is the following :

I ploted the given focus(3,1) and graphed the directrix x=1,knowing the e = c/a = sqrt(2)/2 --> c =sqrt2 & a =2 .But since 0<e<1 - so this is an Ellips(correct?)

The length of the major axis is 2a = 2(2)=4 ...

The equation is :


IS MY WORK CORRECT ? MISSING SOMETHING? - Thanks in advance-

Aladdin

[Honeysuckle588]

For whatever reason, your equation is not rendering on my machine. How did you type it in?

[Aladdin]

For whatever reason, your equation is not rendering on my machine. How did you type it in?

Sorry, my mistake - The equation is :

[Honeysuckle588]

I'm sorry that I got distracted and didn't reply sooner. Is your "equation" of the directrix correct? As is, it looks like an inequality?

[Honeysuckle588]

I see how you got a=2 and c = sqrt(2). Then, the length of the major axis would certainly be 4. How did you translate this information into your equation? What steps did you follow?

[Aladdin]

The equation of the directrix is x-1 = >0 ( it says it's positive)

The center of the ellips is at (1,1) ??

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2)

[Honeysuckle588]

I thought the directrix was a line. So I assumed it was the line x-1=0 which implies x = 1. That is, a vertical line. If this is the case, then the center of the ellipse can't be at (1,1).

Am I misunderstanding something?

[Aladdin]

I need to find the center right ?

[Honeysuckle588]

Yes. You need the center and the value of a and b.

[Aladdin]

Thanks, I appreciate your hard work.