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

Sagot :

culveryolanda46

Step-by-step explanation:

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

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)

[tex] {c}^{2} = {a}^{2} - {b}^{2} [/tex]

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

[tex] {c}^{2} = 9 - 4[/tex]

[tex] {c}^{2} = 5[/tex]

[tex]c = \sqrt{5} [/tex]

So our foci is

[tex](2, - 5 + \sqrt{5} )[/tex]

and

[tex](2, - 5 - \sqrt{5} )[/tex]

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