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# I need help with this question please!

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3 May 12, 2019

#1
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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   May 12, 2019
#3
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(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!!!!   May 12, 2019