## Avva Group Title 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 2 years ago 2 years ago

1. experimentX Group Title

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

2. experimentX Group Title

solve this, you might get the answer

3. Avva Group Title

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 Group Title

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 Group Title

5 minutes

6. Avva Group Title

TYT :)

7. ash2326 Group Title

@Avva do you know what is an ellipse?

8. ash2326 Group Title

9. Avva Group Title

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 Group Title

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 Group Title

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

12. Avva Group Title

yes

13. ash2326 Group Title

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 Group Title

OK , until now I understand both definition

15. Avva Group Title

definitions

16. ash2326 Group Title

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 Group Title

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

18. Avva Group Title

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 Group Title

Yeah that's right:D

20. Avva Group Title

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

21. ash2326 Group Title

Welcome @Avva F1???

22. Avva Group Title