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SIZIF [17.4K]
1 year ago
5

which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9

Mathematics
1 answer:
elena55 [62]1 year ago
6 0

Step-by-step explanation:

\frac{(x - 2) {}^{2} }{4}  +  \frac{(y + 5) {}^{2} }{9}  = 1

This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a

The formula for the foci of the vertical ellipse is

(h,k+c) and (h,k-c).

where c is

Our center (h,k) is (2, -5)

{c}^{2}  =  {a}^{2}  -  {b}^{2}

Here a^2 is 9, b^2 is 4.

{c}^{2}  = 9 - 4

{c}^{2}  = 5

c =  \sqrt{5}

So our foci is

(2, - 5 +  \sqrt{5} )

and

(2, - 5 -  \sqrt{5} )

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