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Question 1

I don't know what I'm doing with this one haha Question 2 Nov 5, 2019
edited by Guest  Nov 6, 2019

#1
+2

The  equation in the first problem is impossible....here's why...

If the center   is  (-2,4)  and a vertex is  (-2, 7)    then the major axis  lies  on the line  x  = -2...so this hyperbola will intersect the y axis

So "a"   =  3

So     the correct form  would  have to be

(y - 4)^2          (x + 2)^2

______     -    ________  =   1

a^2                  b^2

The  positive slope  of  one  asymptote for this hyperbola   is  given by   a / b

So

3/b  = 1/2

This implies that  "b"  = 6

Therefore....the correct  equation is

(y - 4)^2          ( x + 2)^2

_______   -    _________   =   1

9                    36

Here is the graph :   https://www.desmos.com/calculator/a9eebyh8du   Nov 6, 2019
#2
+1

Second one

The center  is    (h, k)  =  ( 6, -4)

a  = sqrt (36)  = 6       b   =  sqrt (49)   =  7

This hyperbola intersects the y axis

The  slope  of  the  asymptotes  =    ±√[36/49]  =   ±(6/7)

The equation of the asymptotes  is

y - k =  ±(a/b) ( x - h)

so

y + 4 =  ±(6/7)(x - 6)

Here's a graph :  https://www.desmos.com/calculator/kalxu48bwq   Nov 6, 2019