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Find the center, vertices, and foci of the ellipse with equation 4x2 + 6y2 = 24.

1 Answer

6 votes
we have that

4x² + 6y² = 24
divide everything by 24

4x²/24 + 6y/24² = 24/24--------> x²/6 + y²/4 = 1
a²=6------> a=√6
b²=4------> b=2

a>b----------> the major axis is parallel to the x-axis

the center is the point (0,0)
(h,k) is (0,0)

c²=a²-b²
c²=6-4
c=√2

vertices:
(h-a,k) and (h+a,k)
(0-√6, 0) and (0+√6, 0)
(-√6, 0) and (√6, 0)

Foci:
(h-c, k) and (h+c, k)
(0-√2, 0) and (0+√2, 0)
(-√2, 0) and (√2, 0)


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