Persamaan salah satu asimtot dari hiperbola : 4y² - x² + 16y + 6x + 3 = 0 adalah...

karena y(+) dan x(-), persamaan hiperbolanya
(y-q)^2/b^2 - (x-p)^2/a^2 = 1

4y^2 - x^2 + 16y + 6x +  3 = 0
4y^2 + 16y - x^2 + 6x = -3
4(y^2+4y) - (x^2 - 6x) = -3
4(y+2)^2-4 - (x-3)^2-9 = -3
4(y+2)^2 - (x-3)^2 = 10
(y+2)^2/(5/2) - (x-3)^2/10 = 1

persamaan asimtot
(y-q)^2/b^2 - (x-p)^2/a^2 = 0
(y+2)^2/(5/2) - (x-3)^2/10 = 0
(y+2)^2/(5/2) = (x-3)^2/10
10((y+2)^2) = (5/2)(x-3)^2
akar10(y+2) = +- akar(5/2)(x-3)

asimtot 1
akar10(y+2) = akar(5/2)(x-3)
akar10y + 2akar10 = akar(5/2)x - 3akar(5/2)
akar10y - akar(5/2x) + 2akar10 + 3akar(5/2) = 0

asimtot 2
akar10(y+2) = -akar(5/2)(x-3)
akar10y + 2akar10 = -akar(5/2)x + 3akar(5/2)
akar10y + akar(5/2x) + 2akar10 - 3akar(5/2) = 0

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