anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
experimentX
  • experimentX
0.5*(x-y+3)^2/(1+1) = (x+1)^2+(y+1)^2
experimentX
  • experimentX
solve this, you might get the answer
anonymous
  • anonymous
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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experimentX
  • experimentX
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
ash2326
  • ash2326
5 minutes
anonymous
  • anonymous
TYT :)
ash2326
  • ash2326
@Avva do you know what is an ellipse?
ash2326
  • ash2326
Avva please reply to my question?
anonymous
  • anonymous
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??
ash2326
  • ash2326
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.
ash2326
  • ash2326
Here we need a somewhat different definition of ellipse, Are you here?
anonymous
  • anonymous
yes
ash2326
  • ash2326
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
anonymous
  • anonymous
OK , until now I understand both definition
anonymous
  • anonymous
definitions
ash2326
  • ash2326
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
anonymous
  • anonymous
\[\sqrt{(x+1)^{2}+(y+1)^{2}}\]
anonymous
  • anonymous
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 ??
ash2326
  • ash2326
Yeah that's right:D
anonymous
  • anonymous
ok Thank You ash for your time and your efforts ,, you have been always my F1 :))
ash2326
  • ash2326
Welcome @Avva F1???
anonymous
  • anonymous
In any software when you seek help you press F1 :D
ash2326
  • ash2326
That's creative Avva:)
anonymous
  • anonymous
Thank You ash :) ,, you are brilliant Bro

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