Persamaan salah satu asimtot dari hiperbola : 9x^2 - 36x - 4y^2 - 8y - 4 = 0 adalah....

9x^2 - 36x - 4y^2 - 8y - 4 = 0
9x^2 - 36x + .... - 4y^2 - 8y - 4 = 0 + ....
9(x^2 - 4x + .... ) - 4(y^2 + 2y + 1) = 0 + ....
9(x^2 - 4x + 4) - 4(y + 1)^2 = 0 + 36
9(x - 2)^2 - 4(y + 1)^2 = 36 ====> kedua ruas dibagi 36
(x - 2)^2 / 4 - (y + 1)^2 / 9 = 1
Persamaan Asimtot
(y + 1)^2 / 9 = (x - 2)^2 / 4
(y + 1)^2 = (9/4) (x - 2)^2
(y + 1) = ± (3/2) (x - 2) ======> kedua ruas kali 2
2y + 2 = ± 3(x - 2)
(+) 2y + 2 = 3(x - 2)
=> 2y + 2 = 3x - 6
=> -3x + 2y + 8 = 0
=> 3x - 2y - 8 = 0
(-) 2y + 2 = -3(x - 2)
=> 2y + 2 = -3x + 6
=> 3x + 2y - 4 = 0