Question

What is the equation of an ellipse with foci at (-4, 0) and (-4, -6) and major axis of 10? I believe my answer is wrong so please help me :)

Answer 1

please help ! :)

Answer 2

since the x values there are the same; we now it streches along a y axis parallel line

Answer 3

half the distance between foci to find the distance to the center.. 0 - -6 = 6

6/2 = 3

the center is at (-4,-3) then

Answer 4

i believe "major axis of 10" means the distance from tip to tip; so that leaves us with 5 from center to the outer vertex

Answer 5

x^2 y^2
---- + ---- = 1
s^2 L^2

L^2 = 5^2 = 25



x^2 y^2
---- + ---- = 1
s^2 25

s^2 = Maj axis distance^2 - foci distance^2

s^2 = 5^2 - 3^2

s^2 = 25 - 9 = 16
----------------------

x^2 y^2
---- + ---- = 1
16 25

now when x = 0; y = +-5, and when y=0 x=+-4; but we have to put back over in its original spot; right now its at the origin

Answer 6

(x+4)^2 (y+3)^2
-------- + -------- = 1
16 25

Answer 7

the 16 and 25 are backwards :)

Answer 8

no they arent...y is the major; never mind that idiot in the back of my head :)

Answer 9

Here is a ref sheet for ellipses, hyperbolas that might help you

Answer 10

wha!?! theres already stuff out for this ;)

Answer 11

Thank you both so much! That all really helped me!! I appreciate all of the help :)