Question

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

Answer 1

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

Answer 2

solve this, you might get the answer

Answer 3

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 ??

Answer 4

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

Answer 5

5 minutes

Answer 6

TYT :)

Answer 7

@Avva do you know what is an ellipse?

Answer 8

Avva please reply to my question?

Answer 9

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??

Answer 10

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.

Answer 11

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

Answer 12

yes

Answer 13

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

Answer 14

OK , until now I understand both definition

Answer 15

definitions

Answer 16

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

Answer 17

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

Answer 18

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 ??

Answer 19

Yeah that's right:D

Answer 20

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

Answer 21

Welcome @Avva F1???

Answer 22

In any software when you seek help you press F1 :D

Answer 23

That's creative Avva:)

Answer 24

Thank You ash :) ,, you are brilliant Bro