equations of the ellipse (1 Viewer)

[superSAIyan2]

Hey guys

Can you help me with these questions:

Find eqn of ellipse with

a) Focus (3,0) directrix x = 6, eccentricity = 1/2
when i equate ae=3 and a/e=6 i get different values for a. Is the directrix wrong. Or is centre not(0,0)

Similarly
b) Focus 1,0) D:x=9 and e=3/5

Thanks

 

[Parvee]

You have to assume that the centre is not at (0,0)
Therefore you start with:
Focus: h+ae=3
Directrix: h+a/e=6
and you just use simultaneous which gives you h=2 and a=2

 

[superSAIyan2]

so if (x-h)^2/a^2 + (y-k)^2/b^2 = 1 is the ellipse
since focus is one xaxis therefore k = 0, and a = 2 and h=2
do u then use b^2 = a^2(1-e^2) = 3
so then u sub the values to find the eqn ofellipse?

 

[Parvee]

so if (x-h)^2/a^2 + (y-k)^2/b^2 = 1 is the ellipse
since focus is one xaxis therefore k = 0, and a = 2 and h=2
do u then use b^2 = a^2(1-e^2) = 3
so then u sub the values to find the eqn ofellipse?

You already know your a,b,h and k value. So from this you can just form your equation because you know the equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 =1

 

[superSAIyan2]

oh ok thanks a lot ... btw isnt it (y-k)^2/b^2 ?

 

[Parvee]

oh ok thanks a lot ... btw isnt it (y-k)^2/b^2 ?

yeah
made a typo