# Equation of ellipse

Tags:
1. Oct 21, 2015

### Yatin

Find the equation of the ellipse whose eccentricity is 2/3 and which has (2,0) and x+y=0 for focus and corresponding directrix .

given answer: (x-2)^2 + y^2 = 4/9 ( ( (x+y)/√2)^2)

what i tried doing:-

ae=2
⇒a*2/3=2
∴a=3

found b=√5.

2. Oct 21, 2015

### Staff: Mentor

Have you drawn a sketch of the ellipse? Based on the given information, the major axis of the ellipse is a line with slope 1 that goes through the point (2, 0). You will need to know how to write the equation of an ellipse that is not in standard orientation. The rotation is the reason for the xy term in the equation.

Also, in future posts, please do not delete the three parts of the homework template.

3. Oct 22, 2015

### Yatin

Thanks a lot Mark.

4. Oct 22, 2015

### HallsofIvy

Staff Emeritus
You started by calculating a value of some number, "a". Why? What does "a" mean? The fact that you did that must mean that you have some formula that involves "a". What is that formula?

5. Oct 22, 2015

### Yatin

Thanks for taking interest in my thread HallsofIvy.

'a' represents the semimajor axis of the ellipse.
'b' represents the semiminor axis.
e: eccentricity
Foci : + or - ae ( since there r 2 foci.)

I realised that finding a or b, however, was unnecessary.

Last edited: Oct 22, 2015