The equation of the ellipse is x^2/4 + y^2/25 = 1.
The questions I have are:
1) is this ellipse vertical, as in the foci are on the y-axis?
2) is the major axis on the y-axis?
3) are the directrices vertical or horizontal?
I have for working out:
a^2=4, b^2=25
b^2=a^2(1-e^2)
25 =4(1-e^2)
25/4 = 1 - e^2
21/4 = e^2 (e^2 is (+)ve because e is a lenght)
e = (sq rt) of 21 over 4
Foci= (0, +/- (sq rt) 21)
Directrices= +/- 10/(sq rt) 21
now if the directrices are horizontal then they are y= +/- 10/(sq rt 21) which is
+/- ~2.18. if the directrices are y= +/- ~2.18 then they will pass through the ellipse.??? Something must be wrong here.
Any help will be greatly appreciated. Thank you.
The questions I have are:
1) is this ellipse vertical, as in the foci are on the y-axis?
2) is the major axis on the y-axis?
3) are the directrices vertical or horizontal?
I have for working out:
a^2=4, b^2=25
b^2=a^2(1-e^2)
25 =4(1-e^2)
25/4 = 1 - e^2
21/4 = e^2 (e^2 is (+)ve because e is a lenght)
e = (sq rt) of 21 over 4
Foci= (0, +/- (sq rt) 21)
Directrices= +/- 10/(sq rt) 21
now if the directrices are horizontal then they are y= +/- 10/(sq rt 21) which is
+/- ~2.18. if the directrices are y= +/- ~2.18 then they will pass through the ellipse.??? Something must be wrong here.
Any help will be greatly appreciated. Thank you.