Determine equation for the line that passes through points

Question

1). Points (8,-5) and (2,1) are endpoints of diameter of the circle.
(a) Compute the equation of the circle?

2). Given y=3sin(4x-Π
(a). Define the Phase Shift

3). Let f(x)= {3x² +3}/{x² -4}
(a). Write the domain
(b). Write the vertical asymptote(s).
(c). Write the horizontal asymptote.

4). Determine equation for the line that passes through points (4,6) and (-5,9). Write equation in slop-intercept form. Illustrate Work.

5). Consider f(x) = 4x² - 7 and g(x) = x-3
(a). Determine (fog) (-2) Show Work.