Question

The equation of an ellipse is given by.
(x-2)^2/36+(y+5)^2/100=1
Identify the coordinates of the center of the ellipse.
Find the length of the major and minor axes.
Graph the ellipse.
Label the center.

Answer 1

PLEASE HELP ME !!!!!!!!! Im working late hours to get my work done, i really need help on this

Answer 2

\[\Large \frac{(x-2)^2}{36}+\frac{(y+5)^2}{100}=1\]
is the same as
\[\Large \frac{(x-2)^2}{36}+\frac{(y-(-5))^2}{100}=1\]

Answer 3

Notice how
\[\Large \frac{(x-2)^2}{36}+\frac{(y-(-5))^2}{100}=1\]
is in the form
\[\Large \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\]
where
a = 6
b = 10
h = 2
k = -5

Answer 4

The center is (h,k) = (2,-5)

Answer 5

Kinda ! i never new how to do this kind of work so i kinda dont know anything about it

Answer 6

a = 6 so 2*a = 2*6 = 12
b = 10 so 2*b = 2*10 = 20

the minor axis is 12 units long
the major axis is 20 units long

the major axis corresponds to b, the b is under the y term, so the major axis is vertical (completely straight up and down) making the ellipse look like this

Answer 7

You can use desmos to graph

https://www.desmos.com/calculator/ivvthvilhu

Answer 8

So im kinda confused lol this is all the first question ? then i use that website to graph ?

Answer 9

in circles the general centre radius form is
\[(x-h)^2 +(y-k)^2 = r^2\] where (h,k) is the centre.

For an ellipse this is
\[\frac{ (x-h)^2 }{ a^2 }+\frac{ (y-k)^2}{ b^2 } = 1\] for centre (h,k)

Answer 10

IF a > b, the length of the major axis is 2a units long and the length of the minor axis is 2b units long.

If a < b the the length of the major axis is 2b units long and " " is 2a units long.

Answer 11

@medina13 yes the question is broken up into 3 parts basically