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Analytic Geometry -----> Ellipse Find the equation of ellipse whose focus is (-1,-1) and the corresponding directrix is x-y+3=0 and e=0.5

Mathematics
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0.5*(x-y+3)^2/(1+1) = (x+1)^2+(y+1)^2
solve this, you might get the answer
Thank you for replying me But if you please illustrate what did you do ?? because I can't understand the equation of the given directrix why it has X and Y ??

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Other answers:

x, y is a point on ellipse (x-y+3)^2/(1+1) is the distance from point to directrix so multiply it by eccectricity and on the right hand side you have distance formula .. from foci to point on ellipse hope you understand
5 minutes
TYT :)
@Avva do you know what is an ellipse?
Avva please reply to my question?
am awfully Sorry ash I was away , yes I know an ellipse is a set of points where the sum of distances from a point on it to two fixed points (two foci) is constant = 2a right??
An ellipse is the set of points in the plane, the sum of whose distance from two fixed points is a given positive constant that is greater than the distance between the two fixed points.
Here we need a somewhat different definition of ellipse, Are you here?
yes
Ellipse can also be defined as the locus of points whose distance from a fixed point and a line are in a fixed ratio. The point is one of the focus and the line is the directrix of ellipse. The ratio is the eccentricity of the ellipse
OK , until now I understand both definition
definitions
Yeah so in our question the focus is -1,1 . and the directrix is x-y+3=0. Let x,y be a point on the ellipse, just use distance formula and tell me its distance from -1,1
\[\sqrt{(x+1)^{2}+(y+1)^{2}}\]
so we will use the formula distance from p(x,y) to the focus (-1,-1) = e*distance from p(x,y) to its directrix Right ??
Yeah that's right:D
ok Thank You ash for your time and your efforts ,, you have been always my F1 :))
Welcome @Avva F1???
In any software when you seek help you press F1 :D
That's creative Avva:)
Thank You ash :) ,, you are brilliant Bro

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