CONIC SECTION

Posted February 12th, 2010 by alpha

Find the equation to the conic section whose focus is (1,-1), eccentricity is 1/2 and the directrix is the line x-y=3.Is the conic section ellipse?

Comments

On February 12th, 2010 alpha says:

But I do not know how to check that a conic is an ellipse. Which property of the ellipse is to be used?

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``Old theorems never die; they turn into definitions.''
----E. Hewitt

''ALPHA" =)

On February 13th, 2010 Structure says:

$(x-1)^2+(y+1)^2=\frac{1}{4}\frac{(x-y-3)^2}{2}$

$7x^2+2xy+7y^2-10x+10y+7=0$

ellipse center $C=(\frac{5}{6},-\frac{5}{6})$
reduced equation

$\frac{u^2}{\frac{2}{9}}+\frac{v^2}{\frac{1}{6}}-1=0$