Question

Find an equation for the hyperbola that satisfies the following conditions.

Vertices (−1,1) and (1,1); foci 16 units apart .

1=

Answer 1

General curve with centre origin is shown

Distance between foci = 16

That is we know distance between foci is 2c

So 2c=16

C=8

Vertices (-1,1) and (1,1) and is of the form (-a,1) ,(a,1)

So a= 1

If we chech the point it is clear that hyperbloa is shifted along y axis 1 unit

Clearly the axis is parallel to x axis

General equation is

h,k is the center of hyperbola which the average of two verices

(-1,1) and (1,1) centre (0,1)=(h,k)

So equation of hyperbola is

h=0,k=1

a=1 b=√63

Which is the equation of hyperbola