Question

9x^2-4y^2-18x-8y-31=0.
Tentukan unsur unsur dari persamaan hiperbola dan grafiknya! Please help me!

Answer 1

9x² - 18x - 4y² - 8y = 31
9(x² - 2x) - 4(y² +2y) = 31
9(x-1)² - 4(y+1)² = 31 +9- 4 = 36
(x-1)²/4  - (y+1)²/9  = 1
a² = 4 --> a= 2
b² = 9 --> b = 3
c= √(a²+b²)= √13
Pusat (p,q) = (1, -1)
F₁ (p+c, q) = {(1+√13),-1 }
F₂(p-c), q)= {(1-√13), -1}
Puncak A₁ = (p+a , q)= (3, -1),
Puncak A₂ = (p-a, q)= (-1, - 1)
sumbu nyata y = - 1