+128460 First one
Center = (1,4) = (h, k)
Since the transverse axis is parallelto the y axis, the hyperbola opens up and down
The form is
(y - k)^2 (x -h)^2
______ - _________ = 1
a^2 b^2
a = 20/2 = 10 ⇒ a^2 = 100
b = 16/2 = 8 ⇒ b^2 = 64
So.....the equation is
(y - 4)^2 (x - 1)^2
______ - _______ = 1
100 64
Here's the graph :
https://www.desmos.com/calculator/ppuyhib2r6
+128460 Second one.....the easiest way to see this one is to note what happens to the lead term of each polynomial as we approach either a large negative or a large positive
1. As - 2x^3 approaches some large negative value.....the limit of the polynomial approaches positive infinity.....so.....True is correct!!!
2. As 2x^4 approcahes some large positive value......the polynomial approaches positive infinity......so....True is correct
3. As -9x^5 approaches some large positive value, the polynomial approaches negative infinity....so.... True is correct
+128460 Third one
(x + 2)^2 ( y + 8)^2
_______ + _________ = 1
16 81
Center (-2, -8)
The major axis = 2sqrt (81) = 2 * 9 = 18 units long....so....the enpoints of the major axis are 18/2 = 9 units from the center
The minor axis = 2sqrt(16) = 2 * 4 = 8 units long....so....the endpoints of the minor axis are 8/2 = 4 units from the center
The endpoints are ( -2 + 4 , -8) ( -2 - 4, -8) ( - 2, -8 + 9) (-2, -8 - 9) =
(2, -8) ( -6, -8) (-2, 1) (-2 - 17)
Connect these with a smooth curve to graph the ellipse....here it is :
https://www.desmos.com/calculator/jwlnfr0asu
