(x+7)^2/36+(y-2)^2/121=1

Question

define these things:

a. Center

b. Vertices

c. Length of minor axis

d. Length of the major axis

e. Foci

Answer 1

a)

(x + 7)² / 36 + (y - 2)² / 121 = 1

The ellipse equation form = (x - h)² / a² + (y - k)² / b² = 1

The center is (h , k)

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

h = -7 , k = 2.

Therefore the center is (-7 , 2).

Answer 2

b)

(x + 7)² / 36 + (y - 2)² / 121 = 1

The ellipse equation form = (x - h)² / b² + (y - k)² / a² = 1

The vertices (h , k + a) , (h , k - a)

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

h = -7 , k = 2 , a² = 121 then a = 11

The vertices is (-7 , 2 + 11) , (-7 , 2 - 11)

Simplify

The vetices (-7 , 13) and (-7 , -9).

 

 

Answer 3

c)

(x + 7)² / 36 + (y - 2)² / 121 = 1

The ellipse equation form = (x - h)² / b² + (y - k)² / a² = 1

The length of minor axis b

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

b^2 = 36

Take sqrt to each side

b = 6

The length of the minor axis : 6.

Answer 4

d)

(x + 7)² / 36 + (y - 2)² / 121 = 1

The ellipse equation form = (x - h)² / b² + (y - k)² / a² = 1

The length of major axis a

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

a² = 121

Take sqrt to each side

a = 11

The length of the major axis : 11.

Answer 5

e)

(x + 7)² / 36 + (y - 2)² / 121 = 1

The ellipse equation form = (x - h)² / b² + (y - k)² / a² = 1

The foci (h , k + c) , (h , k - c) where c = a^2 - b^2

The given equation is (x -(-7))² / 36 + (y - 2)² / 121 = 1

h = -7 , k = 2 , a² = 121 then a = 11, b^2 = 36 then b = 6

c^2 = a^2 - b^2 = 121 - 36 = 85

Take square root to each side

c = √85

The foci is (-7 , 2 + √85) , (-7 , 2 - √85).