Conic Sections

First one.....the major axis lies along y

So

24  =  a^2

sqrt (24)  = sqrt (4 * 6)    =  s sqrt (6)  =  a

The major axis   = 2a =  2  (2sqrt (6) ) =   4sqrt (6)

The minor axis lies along  x

So

12 =  b^2

sqrt (12)  =sqrt ( 4 * 3)  =  2sqrt (3)  = b

The minor axis  = 2b = 2 ( 2 sqrt (3)) = 4 sqrt ( 3)

Second one

center  =  ( 1,6)

focus  = (-1, 6)    means that c   = 2

vertex  (6,6)   means that a  =  5 ⇒   a^2 = 25

And b^2  = a^2 - c^2 =  5^2 - 2^2  = 21

So....the equation is

( x - 1)^2            ( y - 6)^2

_______   +     _________   =     1

    25                     21