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It is known that the center of the ellipse C is at the origin, the focus is on the x-axis, one of its vertices is (0,1), and the eccentricity is equal to 2 / 5 of the original number 5 (1) Please write down the specific process!
Let the standard equation of ellipse C be: X & # 178; / A & # 178; + Y & # 178; / B & # 178; = 1
According to the meaning of the title: A & # 178; - B & # 178; = C & # 178;
b=1,
e=c/a=2√5 / 5
The solution is a = √ 5, B = 1, C = 2
The standard equation of ellipse C: X & # 178 / 5 + Y & # 178; = 1
The quadrilateral ABCD is inscribed in the ellipse x ^ 2 / 9 + y ^ 2 / 16 = 1, where a (3,0) B (0,4) finds the maximum area of quadrilateral ABCD
Quadrilateral ABCD, X2 / 9 + Y2 / 16 = 1,
a=3,b=4,
The focus of the ellipse is on the y-axis, so only when the edges of the quadrilateral ABCD area are fixed, the quadrilateral ABCD area has the maximum value
Then the coordinates of B and D are B (0, - 4) and D (- 3,0)
The maximum area of quadrilateral ABCD = 4 * 1 / 2 * 4 * 3 = 24
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