Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24.

We have that

4x² + 6y² = 24
divide everything by 24

4x²/24 + 6y/24² = 24/24> x²/6 + y²/4 = 1
a²=6> a=√6
b²=4> b=2

a>b>  the major axis is parallel to the x-axis

the center is the point (0,0)
(h,k) is (0,0)

c²=a²-b² 
c²=6-4
c=√2 

vertices:
(h-a,k) and (h+a,k) 
(0-√6, 0) and (0+√6, 0) 
(-√6, 0) and (√6, 0) 

Foci: 
(h-c, k) and (h+c, k) 
(0-√2, 0) and (0+√2, 0) 
(-√2, 0) and (√2, 0) 

B. y=(5x)/(1 + 2x^2)

Step-by-step explanation:

A. y = (5x)/(x * x^2)

Vertical Asymptotes: x = 0

B. y = (5x)/(1 + 2x^2)

Vertical Asymptotes: None

C. y = (5x - 1)/x

Vertical Asymptotes: x = 0

D. y = x/(1 - x^2)

Vertical Asymptotes: x = -1, 1