Avva 3 years ago 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

1. experimentX

0.5*(x-y+3)^2/(1+1) = (x+1)^2+(y+1)^2

2. experimentX

solve this, you might get the answer

3. Avva

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 ??

4. 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

5. ash2326

5 minutes

6. Avva

TYT :)

7. ash2326

@Avva do you know what is an ellipse?

8. ash2326

9. Avva

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??

10. 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.

11. ash2326

Here we need a somewhat different definition of ellipse, Are you here?

12. Avva

yes

13. 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

14. Avva

OK , until now I understand both definition

15. Avva

definitions

16. 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

17. Avva

$\sqrt{(x+1)^{2}+(y+1)^{2}}$

18. Avva

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 ??

19. ash2326

Yeah that's right:D

20. Avva

ok Thank You ash for your time and your efforts ,, you have been always my F1 :))

21. ash2326

Welcome @Avva F1???

22. Avva

23. ash2326

That's creative Avva:)

24. Avva

Thank You ash :) ,, you are brilliant Bro