Question

9x2+4y2 = 36

The foci are located at:
O(-V5,0) and (V5, 0)
0 (-V13, 0) and (V13, 0)
0 (0, -V5) and (0, V5)

Answer 1

The foci of the given ellipse = (0 ,-√5 ) and ( 0, √5 )

Explanation:

Step(i):-

Given Ellipse 9 x² + 4 y² = 36

`(9x^(2) )/(36) + (4y^(2) )/(36) =1`

⇒
`(x^(2) )/(4) + (y^(2) )/(9) = 1`

Step(ii):-

The Major axis lies on y-axis

Foci of the Formula C² = a² -b² = 9-4 =5

C = √5

The Foci is always lie on the major axis(longest) axis, spaced equally each side of the centre

Given ellipse of the foci is lie on Y- axis

Final answer:-

The foci of the given ellipse = (0 ,-√5 ) and ( 0, √5 )