Question

What are the foci of the following graph?
Answers:

(0,-sqrt27 ) and (0,sqrt27 )

(-3, 0) and (3, 0)

(-6, 0) and (6, 0)

(0, -6) and (0, 6)

Answer 1

@CCollet

Answer 2

okay so if the it's elongated along the x-axis then the foci will be on the x-axis and vice versa if its elongated on the y-axis.

so since yours is along the y-axis the points will be (0, -c) and (0, c) where
\[c ^{2} = a^{2} - b^{2}\]
if they were along the x-axis the points would b (-c, 0) and (c, 0) still using the same equation to find c.

Answer 3

So B is the answer? @CCollet

Answer 4

no, if you look at the graph you can see that a = 6 and b is = 3 so the answer you would need is:

\[c = \sqrt{6^{2} - 3^{2}}\]

Answer 5

Ohhh ok so C am I right? @CCollet

Answer 6

\[ c = \sqrt{36 - 9} = \sqrt{27}\]
so the foci are at \[(0,\pm\sqrt{27}) \]

Answer 7

Thank You!