Question

Which of the following expresses the coordinates of the foci of the conic section shown below? ((x-2)^2/4)+((y+5)^2/9)=1

Answer 1

Do you know what type of conic this is?

Answer 2

No

Answer 3

It is an ellipse. The ellipse is has a general equation of the form\[\frac{ (x-h)^{2} }{ a^2 }+\frac{ (y-k)^{2} }{ b^2 }=1\]or\[\frac{ (x-h)^{2} }{ b ^{2} }+\frac{ (y-k)^{2} }{ a ^{2} }=1\]depending upon which is the major vertex and which is the minor. The a is ALWAYS bigger than the b, and whichever axis the a is under is the major one. Here, the 9 is under the y axis, so the y axis is the major vertex and the x is the minor.

Answer 4

The equation for finding the foci is \[a ^{2}-b ^{2}=c ^{2}\]Our a^2 is 9, our b^2 is 4, so\[9-4=c ^{2}\]and \[c=\sqrt{5}\]The foci always lie on the major vertex which is y, so the square root of 5 goes in for the y coordinate. But don't forget you're not at the center so you have to move the foci according to the center's coordinates.

Answer 5

Okay I thought that was it so is it2, -5 sq rt5 Or 2 sq rt 5, -5?

Answer 6

Isn't it the first one?

Answer 7

Isn't it the first one?

Answer 8

Isn't it the first one?