9x^2+18x-16y^2-32y-151=0

Bab Irisan Kerucut
Matematika SMA Kelas XI

9x² + 18x - 16y² - 32y - 151 = 0
9(x² + 2x) - 16 (y² + 2y) = 151
9(x + 1)² - 16(y + 1)² = 151 + 9 . 1² - 16 . 1²
9(x + 1)² - 16(y +1)² = 144
(x + 1)² / 16 - (y + 1)² / 9 = 1

a² = 16
a = +- 4

b² = 9
b = +- 3

persamaan asimtot =
(y - k) = +- (b/a) (x - h)
y + 1 = +- (3/4) (x + 1)

y + 1 = (3x + 3)/4
y = (3x + 3)/4 - 1
y = (3x - 1)/4

atau

y + 1 = - (3x + 3)/4
y = (-3x - 3)/4 - 1
y = (-3x - 7)/4

Jawab:
________
9x^2+18x-16y^2-32y-151=0
Dik:
a = 9
b= 18
c= (−16y^2 −32y−151)

9(x^2+2x+ -16y^2 -32y-151/9)
9(x^2+2x+1-1 + -16y^2-32y-151/9)
9(x+1)^2 -1 + -16y^2-32y-151/9)
9(x+1)^2 + -16y^2-32y-151/9 -1
9(x+1)^2 + 9(-16y^2-32y-151/9 -1)
9(x+1)^2 + 9(-16y^2-32y-151/9 -1)=0
9(((x+1)^2) + -16y^2-32y-151/9 -1=0
(x+1)^2 + -16y^2-32y-151/9 -1=0
(x+1)^2 -1 = - -16y^2-32y-151 /9
(x+1)^2 = - -16y^2-32y-151/9 + 1
x+1 = +- √- -16y^2-32y-151/9 + 1
x= √- -16y^2-32y-151/9+1-1, -√- -16y^2-32y-151/9 + 1

*Terima kasih*