+0  
 
0
1
140
5
avatar+1656 

 

2.

 Dec 12, 2019
 #1
avatar+109064 
+1

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

 

 

 

cool cool cool

 Dec 12, 2019
 #2
avatar+1656 
+1

ohh okay i see my mistake thank you!!

jjennylove  Dec 12, 2019
 #3
avatar+109064 
+1

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

 

 

cool cool cool

 Dec 12, 2019
 #4
avatar+109064 
+1

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

 

 

 

cool cool cool

 Dec 12, 2019
 #5
avatar+109064 
+1

Your last one is CORRECT!!!!

 

 

cool cool cool

 Dec 12, 2019

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