Question 1
I don't know what I'm doing with this one haha
Question 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
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