Math help college algebra?

Question

1. Find an equation for the hyperbola with vertices at (0, -4) and (0, 4); asymptote with the line y = (3/4) x

2. Find an equation for the ellipse with foci at (0, -1) and (0, 1); length of the major axis is 6

 

 

Answer 1

1.

The line is y= (3/4)x.

Here the vertices are in the form of (0, ±a)   that is (0,±4).

So, it is vertical hyperbola and the equation for vertical hyperbola is .

Here a = 4 and from the asymptote line equation m = 3/4.

m= a / b =4 / b = 3/4.

Hence, b= 16 / 3.

So,the equation for the hyperbola is .

Hence the equation of hyperbola is .

Answer 2

2.

The foci are at (0,-1) and (0,1)  that  is foci is at (0,±1) ,foci on y-axis and centre is origin.

Hence the value of c=1.

length of the major axis = 6

=> 2*a  =  6.

=>a = 3

.

.

The equation for the ellipse is  .

.

Hence ,the equation of the ellipse is  .