Question

QUESTION FOR THE FOLLOWING GRAPH:
* Identify the coordinates of the center of this ellipse.
* Use the values of a and b to locate the coordinate f the vertices.
* What are the coordinates of the foci?
* Graph this ellipse. Clearly label the foci and vertices

Answer 1

\[\frac{ (x-2)^2 }{ 36 } + \frac{ (y+1)^2 }{ 25 } = 1\]
I know that the center is (2, -1).

Answer 2

I forgot the formula for both foci and vertices.
What I do know is that the foci formula below is for equations with their center at the origin.
\[c^2 = a^2−b^2\] And i thought a^2 was supposed to tell me the vertices from the origin too.

Answer 3

\[b ^{2}=a ^{2}\left( 1-e ^{2} \right),25=36\left( 1-e ^{2} \right)\]
\[e ^{2}=1-\frac{ 25 }{36}=\frac{ 11 }{36 }\]
\[e=\frac{ \sqrt{11} }{ 6 }\]
\[foci are \left( \pm ae+x co-ordinate of centre,y co-ordinate of centre \right) i.e.,\left( -\sqrt{11}+2,-1 \right) and \left( \sqrt{11}+2,-11 \right)\]

Answer 4

Uh oh. It went off into the distance... lolz :) But thank you!

Answer 5

What is the formula for vertices when they aren't at the origin?

Answer 6

i write again.they are
\[\left(- \sqrt{11}+2,-1 \right) and \left( \sqrt{11}+2,-1 \right)\]
\[vertices are \left( -a+x co-ordinate of centre ,y co-ordinate of centre \right) and\]
\[\left( a+x co-ordinate of centre, y co-ordinate of centre \right)\]

Answer 7

Thank you! :D

Answer 8

yw

Answer 9

FOCI:
\[(−\sqrt{11}+ 2,−1)and(\sqrt{11}+ 2,−1)\]
VERTICES:
\[(-4,-1) and(8,-1)\]