Question

The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3).
https://hanwingspanps.owschools.com/media/g_alg02_ccss_2015/8/l7elpseq.gif

i need this put into this equation

Answer 1

cool stuff
we have the center is (0,0) then
a is just the length between (0,0) and (5,0) (or the length between (0,0) and (-5,0))
b is just the length between (0,0) and (0,3) ( or the length between (0,0) and (0,-3))

Answer 2

what is x and y then

Answer 3

x and y are variables

Answer 4

without the variables we wouldn't be able to make an ellipse
(x,y) is the point that varies around the ellipse

Answer 5

the only values you need to find are a and b

Answer 6

but x,y are points already given ?

Answer 7

because i need to completely fill in the equation

Answer 8

x-intercepts is where the ellipse pass through the x-axis this is where the y-coordinate will be 0

y-intercepts is wehre the ellipse pass through the y-axis this is where the x-coordinate will be 0


y and x aren't always 0...
I'm trying to say there x and y are variables where as the x-intercepts and y-intercepts are ordered pairs where both coordinates are constant value

Answer 9

the only values you need to find are a and b

Answer 10

x and y stay as they are because they are variables

Answer 11

so i should plot the lnes than =0

Answer 12

no

Answer 13

we have the center is (0,0) then
a is just the length between (0,0) and (5,0) (or the length between (0,0) and (-5,0))
b is just the length between (0,0) and (0,3) ( or the length between (0,0) and (0,-3))


this is all you need to know

Answer 14

find a and b using this

a is the length between the center and the x-intercept
b is the length between the center and the y-intercept
in order words

Answer 15

how far is 5 from 0?
how far is 3 from 0?

Answer 16

a=10 b=6
or
a=5 b=3

Answer 17

where do you get a=10 or b=6?

5 is only 5 units from 0
and
3 is only 3 units from 0

Answer 18

so a=5 and b=3

Answer 19

im going 5 from -5

Answer 20

yeah we don't want to do that...
I can show you a more convincing way I think

earlier you so badly wanted to plug in our x-intercept and y-intercepts
we can do that...
and we can use that to find a and b

\[(5,0) \text{ inset into } \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ \frac{5^2}{a^2}+\frac{0^2}{b^2}=1 \\ \frac{5^2}{a^2}=1 \\ 5^2=a^2 \\ a^2=25 \]
you can use (-5,0) to find a^2 to be 25 also

Answer 21

\[(0,3) \text{ insert into } \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ \frac{0^2}{a^2}+\frac{3^2}{b^2}=1 \\ \frac{3^2}{b^2}=1 \\ 3^2=b^2 \\ b^2=9\]

Answer 22

the ellipse is therefore
\[\frac{x^2}{25}+\frac{y^2}{9}=1 \]

Answer 23

a=5 which is the distance from the x-intercept to the center

b=3 which is the distance from the y-intercept to the center

Answer 24

by showing me the awnser i understand it ten fold

Answer 25

you don't have to do all of that math is what I'm saying
but you can

Answer 26

okay so you only doing from one set point to center not both

Answer 27

for example
here is another problem:
The ellipse with x-intercepts (2,0) and (-2,0); y-intercepts (0,9) and (0,-9)

the distance from x-intercept to center is 2 this is your a
the distance from y-intercept to center is 9 this is your b

Answer 28

but you could do some algebra like I did above to find this

Answer 29

@mathmale close your eyes ive betrayed you

Answer 30

\[\frac{x^2}{2^2}+\frac{y^2}{9^2}=1 \]
would be the answer to my example

Answer 31

do you understand how I got a=2 and b=3?

Answer 32

for my example that is

Answer 33

okay i get it........... thanks once again

Answer 34

np

Answer 35

It would help so much if you, DD, would sketch this parabola. Sketch the four given points, each of which represents a vertex.

Once you've completed this sketch, we can further discuss what a and b mean and where they come from.

Please try to understand the example given you by freckles; it's accurate.

freckles Best Response Medals 1

for example
here is another problem:
The ellipse with x-intercepts (2,0) and (-2,0); y-intercepts (0,9) and (0,-9)

the distance from x-intercept to center is 2 this is your a
the distance from y-intercept to center is 9 this is your b

Answer 36

its been a long day.....i really wish i could thank you in person ......everything and everyone on here is so generous and helpful

Answer 37

The ellipse with x-intercepts at (4, 0) and (-4, 0), y-intercepts at (0, 9) and (0, -9), and center at (0, 0).

a^2=20
b^2=81