Question

The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) and its respective focus at (0, 14). Which equation represents the comet's orbit?

Answer 1

Remember that

If the given coordinates of the vertices and foci have the form (0,10) and (0,14)

then

the transverse axis is the y-axis

so

the equation is of the form

(y-k)^2/a^2-(x-h)^2/b^2=1

In this problem

center (h,k) is equal to (0,4)

(0,a-k)) is equal to (0,10)

a=10-4=6

(0,c-k) is equal to (0,14)

c=14-4=10

Find out the value of b

b^2=c^2-a^2

b^2=10^2-6^2

b^2=64

therefore

the equation is equal to

(y-4)^2/36-x^2/64=1

the answer is option A