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.
Accepted Solution
A:
Answer:vertices: (-7, -3), (-1, -3)foci: (-9, -3), (1, -3)Step-by-step explanation:For a hyperbola of the form ... [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]The vertices are located at (h±a, k), and the foci are located at (h±c, k), where ... [tex]c=\sqrt{a^2+b^2}[/tex]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 graphfoci: (-4±5, -3) . . . . . . . . shown green on the graph