The discussion revolves around finding the equation of an ellipse with a given eccentricity of 2/3, a focus at the point (2,0), and a directrix defined by the line x+y=0. Participants are exploring the relationship between the parameters of the ellipse and its geometric properties.
Some participants have provided insights regarding the geometric interpretation of the ellipse and the implications of the given focus and directrix. Questions about the formulas and the relevance of certain calculations have been raised, indicating an ongoing exploration of the problem.
Participants have noted the importance of adhering to the homework template and the potential impact of the orientation of the ellipse on the equation being derived.
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.Yatin said: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 said: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.
HallsofIvy said: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?