Question

What is the equation of the following graph?

Answer 1

@Michele_Laino

Answer 2

that is a traslated ellipse

Answer 3

as you can see from the graph, the center of our ellipse is located at (0,-2)

Answer 4

y2/9+x2/1

Answer 5

no, since we have to make a traslation

Answer 6

let's consider a new coordinate system X,Y located at point (0,2), namely at the center of your ellipse

Answer 7

with respect to the XY system the equation of our ellipse is:
\[\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1\]

Answer 8

am I right?

Answer 9

yes

Answer 10

here is the situation of your exercise:

Answer 11

oops.. I made a typo, the center of our ellipse is located at poin (0,-2)

Answer 12

and the equations of our traslation are:
\[\Large \left\{ \begin{gathered}
x = X \hfill \\
y = Y - 2 \hfill \\
\end{gathered} \right.\]

Answer 13

okay

Answer 14

now, please solve that system for X, and Y, what do you get?

Answer 15

im lost now.

Answer 16

hint:
we have this:
\[\Large X = x\]
right?

Answer 17

yes

Answer 18

what you want to know?

Answer 19

ok! now do the same, namely write Y as a function of y, please

Answer 20

y=y-2 ?

Answer 21

\[\Large Y = y + 2\]

Answer 22

oh okay

Answer 23

next, replace X with x, and Y with y+2 into my equation above

Answer 24

namely into this equation:
\[\Large \frac{{{X^2}}}{1} + \frac{{{Y^2}}}{9} = 1\]
what equation do you get?

Answer 25

idk im lost again..im glad im going over this other wise i would have gotten this wrong

Answer 26

hint:
\[\Large \frac{{{x^2}}}{1} + \frac{{{{\left( {y + 2} \right)}^2}}}{9} = 1\]
is it right?

Answer 27

yes

Answer 28

that is the requested equation

Answer 29

so that the anwser?

Answer 30

yes!

Answer 31

For shifted one, you need center (h, k), the way to find out a, b as what we had done before. The way a goes with major axis is the same. Just the numerators change to (x-h) ^2 and (y-k)^2.
Dat sit.