This is an ellipse with horizontal major axis.

Its standard form of equation: (x-h)^2+(y-k)^2=1, a>b, (h,k)=(x,y) coordinates of center.

For given ellipse:

center(0,0)

a=5

a^2=25

c=3

c^2=9

c^2=a^2-b^2

b^2=a^2-c^2

b^2=25-9=16

Equation for given ellipse:

x^2/25+y^2/z16=1

..

19. Find the standard form of the equation of the ellipse with minor axis of length 6, center at (5,-1) and a focus at (-1,-1).

This is an ellipse also with horizontal major axis.

Its standard form of equation: (x-h)^2+(y-k)^2=1, a>b, (h,k)=(x,y) coordinates of center.

For given ellipse:

center: (5,-1)

2b=6

b=3

b^2=9

c=(5-1/2=4/2=2

c^2=4

c^2=a^2-b^2

a^2=c^2+b^2=4+9=13

a^2=13

a≈√13≈3.6

Equation for given ellipse:

(x-5)^2/13+(y+1)^2/9=1