Question

which of the following expresses the coordinates of the foci of the comic section shown below?

(x+2)^2 / 64+ (y-1)^2 / 81 = 1

its a circle

Answer 1

\[\frac{ (x+2)^2 }{ 64} + \frac{ (y-1)^2 }{ 81 } = 1\]

Answer 2

well... a circle is just an ellipse with the "a" and "b" components, or the minor and major axis equalling each other

Answer 3

mmmhhh okkk

Answer 4

sooo 8 and 9 then what would i do with this ??

Answer 5

so the foci will be at the "c" distance from the center of the ellipse

notice the BIGGER number is the 81 and that one is under the fraction with the "y" variable
meaning the ellipse is a TALL ellipse, that is the major axis is over the y-axis

and the "c" distance for an ellipse is at \(\bf c=\sqrt{a^2-b^2}\qquad \cfrac{(x-{\color{blue}{ h}})^2}{{\color{brown}{ b}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{brown}{ a}}^2}=1\qquad foci\to ({\color{blue}{ h, k\pm}}c)\)

Answer 6

ok soooo \[c=\sqrt{17}\]

Answer 7

yeap

Answer 8

Foci is \[(-2,1\pm \sqrt{17}\]

Answer 9

yeap

Answer 10

yay omgoshhh thank you for showing me this n_n ! @jdoe0001

Answer 11

yw