Question

find the coordinates of the foci , the vertices , the length of major axis , the minor axis , the eccentricity and length of the Latus rectum of the ellipse x²/36 + y²/16 = 1.​

Answer 1

Given:-

• The ellipse x²/36 + y²/16 = 1.

To find:-

• find the coordinates of the foci , the vertices , the length of major axis , the minor axis , the eccentricity and length of the Latus rectum..?

Solutions:-

• The given is the ellipse x²/36 + y²/16 = 1.

Here,

The denominator of x²/36 is greater than the denominator of y²/16

Therefore,

• the major axis is along the x - axis.
• the minor axis is along the y - axis.

On comparing the given equation with x²/a² + y²/b² = 1

We obtain

• a = 6 and b = 4

=> c = √a² - b²

= √(6)² - (4)²

= √36 - 16

= √20

= 2√5

Therefore,

The coordinates of the fouc are (2√5, 0) and (-2√5, 0)

The coordinates of the vertices are (6, 0) and (-6, 0).

• Length of majar axis => 2a = 2 × 6 = 12
• Length of minor axis => 2b = 2 × 4 = 8

Eccentricity , e = c/a

=> 2√5/6

=> √5/3

Length of Latus rectum => 2b²/a

=> 2 × 16/6

=> 16/3

Hence, the coordinates of the fouc are (2√5, 0) and (-2√5, 0), The coordinates of the vertices are (6, 0) and (-6, 0). Length of majar axis = 12. Length of minor axis = 8, Eccentricity = √5/3, And Length of Latus rectum = 16/3.

Answer 2

Hii :)

Refer to the attachment