Question

Find the location of the center, vertices, and foci for the hyperbola described by the equation.
(x+4)^2/36 - (y-1)^2/25 = 1.

So far I determined that the center is (-4,1)

Answer 1

I dont understand how to find the vertices or foci. I thought I would find a^2 by finding the square root of 36 and b^2 being the square root of 25 (these being the vertices), but this is incorrect as they are not listed as options in the multiple choice.

Answer 2

for example
(x - 2)²/36 + (y + 1)²/25 = 1 can be written (x - 2)² / 6² + (y - -1)² / 5² = 1

and that has the form (x - h)² / a² + (y - k)² / b² where (h, k) is the center

a = 6 > b = 5 → so the major axis is parallel to the x-axis


(I) the center of the ellipse is at (2, -1)

(II) the coordinates of the vertices on the major axis are (2-6, -1) and (2+6, -1) → so at (-4, -1) and (8, -1)

and the coordinates of the vertices on the minor axis are (2, -1-5) and (2, -1+5) → so at (2, -6) and (2, 4)

(III) c = √(a² - b²) = √(6² - 5²) = √[36 - 25] = √11

the coordinates of the foci have the form (h±c, k) → so the coordinates of the foci are at (2-√11, -1) and (2+√11, -1)

(IV) To draw the graph just plot the vertices then sketch the ellipse thru them and show the other stuff they want

Answer 3

i hope this help u.