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Analytic Geometry > Ellipse
Find the equation of ellipse whose focus is (1,1) and the corresponding directrix is xy+3=0 and e=0.5
 2 years ago
 2 years ago
Analytic Geometry > Ellipse Find the equation of ellipse whose focus is (1,1) and the corresponding directrix is xy+3=0 and e=0.5
 2 years ago
 2 years ago

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experimentXBest ResponseYou've already chosen the best response.0
0.5*(xy+3)^2/(1+1) = (x+1)^2+(y+1)^2
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
solve this, you might get the answer
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
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 ??
 2 years ago

experimentXBest ResponseYou've already chosen the best response.0
x, y is a point on ellipse (xy+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
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
@Avva do you know what is an ellipse?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Avva please reply to my question?
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
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??
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
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.
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Here we need a somewhat different definition of ellipse, Are you here?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
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
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
OK , until now I understand both definition
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Yeah so in our question the focus is 1,1 . and the directrix is xy+3=0. Let x,y be a point on the ellipse, just use distance formula and tell me its distance from 1,1
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
\[\sqrt{(x+1)^{2}+(y+1)^{2}}\]
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
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 ??
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
ok Thank You ash for your time and your efforts ,, you have been always my F1 :))
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
In any software when you seek help you press F1 :D
 2 years ago

AvvaBest ResponseYou've already chosen the best response.1
Thank You ash :) ,, you are brilliant Bro
 2 years ago
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