Find the Center the Vertices and the Foci of the ellipse giv

Find the Center, the Vertices, and the Foci of the ellipse given by the equation: 4(x - 5)^2 + 3(y - 4)^2 = 48

Solution

given 4(x-5)²+3(y-4)²=48

((x-5)²/12)+((y-4)²/16) =0

a²=12, b²=16

a=23 , b =4

e=[1-(a²/b²)]

e=[1-(12/16)] =1/2

centre (h,k)=(5,4)

vertices (h,k-b)=(5,4-4),(h,k+b)=(5,4+4)

vertices =(5,0),(5,8)

focie  (h,k-be)=(5,4-2),(h,k+be)=(5,4+2)

focie (5,2),(5,6)