Question

Diketahui persamaan elips x²+4y²-4x-8y-92=0
tentukan :
-koordinat pusat
-koordinat punvak
-titik fokus

Answer 1

X²+4y²-4x-8y-92=0
(x-2)² -4 + 4(y -1)² - 4 -92 = 0
(x-2)² + (y-1)² = 100..................dibagi 100 semua
(x-2)²/100 + (y-1)²/25 = 1

c= √a²-b² = √100-25) = √75 = 5√3
Pusat (2,1)
Puncak (2+10,1) (2-10,1) (2, 1+5) (2,1-5)
              (12,1) (-8, 1) (2, 6) (2, -4)
Fokus   ( 2+5√3, 1)  ( (2-5√3 , 1)