Find Equation of Ellipse | Eccentricity 2/3 | (2,0) Focus & x+y=0 Directrix

[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.

what to do next? please help.

 

[Mark44]

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.

what to do next? please help.

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.

 

[Yatin]

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.

Thanks a lot Mark.

 

[HallsofIvy]

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?

 

[Yatin]

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?

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 realized that finding a or b, however, was unnecessary.