7) What is/are the center, vertices, foci, and
asymptotes of the
hyperbola with the
equation
25x^2 - 4y^2 = 400

Can someone help me, please.

center: (0,0)

vertices: (-4,0) and (4,0)

foci: (-10.8,0) and (10.8,0)

asymptotes: y = -5/2*x and y = 5/2*x

Step-by-step explanation:

Hyperbola with center as origin general equation is:

x²/a² - y²/b² = 1

Our equation is:

25x² - 4y² = 400

Dividing each term by 400:

25x²/400 - 4y²/400 = 400/400

x²/16 - y²/100 = 1

which matches the general equation. Then, the center is (0,0)

a² = 16

a = 4

b² = 100

b = 10

c² = a² + b²

c = √(16+100) = 10.8

General vertices formula: (±a,0). Replacing, the vertices are: (-4,0) and (4,0)

General foci formula: (±c,0). Replacing, the foci are: (-10.8,0) and (10.8,0)

General asymptotes formula: y = ±b/a*x. Replacing, the asymptotes are:

y = -10/4*x = -5/2*x

y = 10/4*x = 5/2*x

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.