fast ellipse qn (1 Viewer)

[blakwidow]

FOr the ellipse x^2/16 + y^2/9 = 1

find e

coordinates of foci

eqn of directrix

parametric eq.

 

[pLuvia]

If I remember correctly
b²=a²(1-e²)

Sub in b and a then solve for e

Spoiler

e=sqrt(7)/4

Foci: (+ae,0)

Spoiler

(+sqrt(7),0)

Directrix: x=+a/e

Spoiler

x=+16/sqrt(7)

Parametric equation: (acos@, bsin@)

Spoiler

(4cos@, 3sin@)

 

[bos1234]

how did you get the last answer??

acos@ , bsin@

a=4,b=3

4cos@,3sin@

??

 

[denoz]

yeah i thought it would be 4cos@, 3sin@ as well because isn't @ just -pi <@< pi

 

[pLuvia]

Yeh, the parametrics are just 4cos@, 3sin@ not that crap I typed

 

[bos1234]

If P(acos@,bsin@) lies on an ellipse and M the directrix has eqn x=a/e and S(ae,0) is focus

then PS = ePM
PS =e(a/e - acos@)
simplifying, a(1-ecos@)

how does S'P = a(1+cos@)

 

[pLuvia]

PS'=ePM'
=e(acos@+a/e)
=a(ecos@+1)

Since the distance from PM' is acos@+a/e