Question

Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16 = 1.

Answer 1

previous was correct

Explanation:

Answer 2

• vertices: (-7, -3), (-1, -3)
• foci: (-9, -3), (1, -3)

Explanation:

For a hyperbola of the form ...

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1`

The vertices are located at (h±a, k), and the foci are located at (h±c, k), where ...

`c=√(a^2+b^2)`

Here, we have (h, k) = (-4, -3), a=3, b=4, and c=√(9+16) = 5.

So, the points of interest are ...

• vertices: (-4±3, -3) . . . . shown red on the graph
• foci: (-4±5, -3) . . . . . . . . shown green on the graph