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