tentukan titik pusat,titik puncak,titik fokus,sumbu mayor,sumbu minor,serta sketsa dari: (x-2)kuadrat/25 +(y+4)kuadrat/4=1

jawab
(x -2)² / (25) + (y+4)² / (4) = 1 → persamaan elip (x -p)²/a² + (y-q)²/b² = 1
p= 2, q = -4
a= 5 , b = 2
c² = a² - b² → c = √(25-4) = √21
Pusat (p, q) = (2, - 4)

Puncak  A {(p+- a), q}, B(p, (q+- b)}
A {(2 +_5), -4} → A1 (7, -4) , A2 (-3, -4)
B { 2, (-4 +_ 2)} → B1 (2, -2) , B2 (2, -6)

Titik Fokus  F { (p+- c , q}= F {(2+_√21, -4}
F1 {2+√21  , -4}
F2 {2-√21, - 4}

sumbu mayor y = q → y = -4
sumbu  minor x = p → x = 2