Question

Please help. Measuring the top half of an ellipse. the top half is 50 feet wide and 18 feet high at the center. Whats the equation?

Answer 1

from the center point, the distance along x and y directions to the curve is 25 an 9 in this case, half of the total width and height

Answer 2

Is that the answer? How did you get to that point?

Answer 3

a = major axis = 25
b = minor axis = 9

the standard ellipse is

( x^2 / a^2) + (y^2 / b^2) = 1

Answer 4

Okay that makes sense, since its half of the answer

Answer 5

so it would be (x^2/25)+(y^2-9) = 1 ?

Answer 6

they say top half,
if you solve for y here you will get

\[y = \pm \sqrt{-x^2 + 1}\]

the top is the plus part

Answer 7

I'm sorry. You lost me.

Answer 8

almost, the 25 is the a value, you can put 25^2

Answer 9

Ohhh okay okay

Answer 10

oh one thing , they measured the top half only, so a = 0.5 * 50 = 5, but b= 18 since it is already half the axis

Answer 11

a = 25
b = 18

Answer 12

oh i forgot about that part

Answer 13

then the equation for only the top half and not the whole ellipse, is the +root

Answer 14

solve that standard form for y and it becomes plus or minus root(-x^2 + 1),

Answer 15

Hold on lost again

Answer 16

sorry that was for a circle, add in the a^2 and b^2 terms, solve for y, and you want just the + root

Answer 17

Why would i have to solve for y?

Answer 18

the , standard ellipse form
x^2 / 25^2 + y^2 / 18^2 = 1

will graph the entire thing, upper and lower half,

solve for y, and you will get a + and a - square root term, the + root graphs the upper half, the - root the bottom half

Answer 19

I thought you didn't have to solve for y in order to create an ellipse? WOuldn't you just need to find the minor and major axis?

Answer 20

if you were going back to graphing it that is

Answer 21

an ellipse is not a function, so you have to break it in half to have y = f(x)

example, graph y^2 = x, or y = plus or minus square root x

+ is upper half, - is lower half

Answer 22

yeah , it is easy to graph it using the axis, but the equation for that graph of the upper half is that + root, they want that equation

Answer 23

so my answer would be the y=+ square root of x2+1 ????????????

Answer 24

hey kat thanks for the help

Answer 25

quick go to my question so i can medal you! ^.^

Answer 26

Okay wonderful

Answer 27

solving for y you get

\[y = \frac{ 18 }{ 25 }\pm \sqrt{625-x^2}\]

Answer 28

and it would be the positive one because its just the top half?

Answer 29

yes, y as a function of x , is that equation, top half is + root , - half negative root

there are other ways to have a more elegant looking equation, but y in terms of x is that

Answer 30

Okay thank you very much. How do i give medals?

Answer 31

or just assume they want the full ellipse, and simply put the 25 and 18 in to the standard form and be done, probably what they want

Answer 32

You think? but I thought putting 25 and 18 will be only the half elipse

Answer 33

not in the x^2/25 + y^2/18 = 1 equation

that represents all points(x,y)

Answer 34

But they only want the top half??

Answer 35

not sure, 'what's the equation?' for the top half only it is that y = + root one
for the whole thing , it is the x^2/25 + y^2/18 = 1

Answer 36

maybe put the x^2/25 + y^2/18 = 1 , and also y >= 0 , to restrict to top

Answer 37

I dont know if thats how it is?

Answer 38

Could you like maybe help me with a different one? Which is probably simpler i'm not getting that one.

Answer 39

@DanJS i have a question that ive seeen that youve already done before, i tagged your name in it. i am sure itd only take a quick 2 minutes tops, if you could please take a quick look itd be greatly appreciated.

Answer 40

not sure, i think you get the ideas though, k tag me in it

Answer 41

It'd be graphing hyperbolas? Do you know how to?