Question

Persamaan hiperbola x² -16y² -4x -32y-28 =0 tentukan koordinat fokus dan puncak

Answer 1

Verified answer

Jawab

x² - 4x - 16y² -32 y = 28
(x² - 4x)  - (16y² + 32y ) = 28
(x ²- 4x) - 16(y² + 2y)= 28
(x - 2)² - 16(y +1)²= 28 + 4  - 16 = 16
(x -2)² - 16(y +1)² = 16
( x - 2)²/16  - (y+1)²/ 1 = 1 → ( x - p)²/a² - (y - q)²/b²= 1
p = 2
q= -1
a² = 16 → a = 4
b² = 1 → b = 1
c= √(a²+b²) = √17

titik pusat (p,q) = (2, -1)
titik  puncak  A1 = (p+a, q) dan A2 = (p-a, q)
A1= (6, -1) 
A2 = (-2, -1)

titik fokus  F1(p+c, q) dan F2 (p-c, q)
F1 = (2 +√17, -1)
F2= (2 - √17, - 1)