Find the end points of the minor and major axis for the graph of the ellipse

Question

Find the end points of the minor and major axis for the graph of the ellipse

(x−2)^2/9+(y−5)^2/36=1

Highest point on the major axis: 

Lowest point on the major axis: 

Rightmost point on the minor axis: 

Leftmost point on the minor axis: 

Answer 1

Given equation of an ellipse:

(x−2)²/9+(y−5)²/36=1

The standard form you need is:

(x−h)²/b²+(y−k)²/a²=1

where:

a>b

2a= the length of the major axis (vertical)

2b= the length of the minor axis (horizontal)

(h,k) = center of ellipse

Therefore:

b² = 9, a²=36

b = 3, a = 6

C(h,k) = (2,5)

The coordinates of the endpoints of the major axis are: (2,5±6)

The coordinates of the endpoints of the minor axis are: (2±3,5)

Highest point on the major axis: (2,11)

Lowest point on the major axis: (2,-1)

Rightmost point on the minor axis: (5,5)

Leftmost point on the minor axis: (-1,5)