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I stuck with this type of questions, could someone please help me with it. Thanks 

 May 12, 2019
 #1
avatar+103982 
+1

I can do some of this

 

(a)  9x^2 -54x -4y^2 -16y + 29 = 0

 

9x^2 - 54x - 4y^2 - 16y  =  -29        complete the square on x and y

 

9(x^2 - 6x + 9) - 4(y^2 + 4y + 4)  =  -29 + 81 - 16

 

9(x - 3)^2  - 4(y + 2)^2  =  36        divide both sides by 36

 

(x - 3)^2  -   (y + 2)^2      

______      ________   =       1

    4                  9

 

The center is  ( 3, -2)   = (h, k)

 

a^2 = 4     so  a  = 2

b^2  = 9    so   a  = 3

 

c  = sqrt ( 4 + 9)  =  sqrt (13)

So....the eccentricity , e   =   c  / a   =   sqrt (13) / 2

 

 

(b)  The foci   are   ( h + c, k)  and (h - c, k)  =      ( 3 + sqrt (13)  , -2)  and  (3 - sqrt(13), -2)

 

The equation of the asymptotes   is    y  =  ±b/a ( x - h) + k    =    ±(3/2)(x - 3) - 2

 

Here's the graph : https://www.desmos.com/calculator/ojovjqb27k

 

cool cool cool

 May 12, 2019
 #2
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Thank you so much. :) 

Guest May 12, 2019
 #3
avatar+103982 
+1

(c)   Parametric form.....this is new to me.....but.....the  parametric form is given by :

 

( h + asec t , k + b tan t )   =   (3 + 2sec t, -2 + 3 tan t )

 

 

(d)  I don't know what this one is asking.....sorry!!!!

 

 

cool cool cool

 May 12, 2019

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