Given that the circle of equation x ^ 2 + y ^ 2 = 9 passes through two focuses and two vertices of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, then the length of the major axis of ellipse is equal to

Given that the circle of equation x ^ 2 + y ^ 2 = 9 passes through two focuses and two vertices of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, then the length of the major axis of ellipse is equal to

Let a > b
If the circle of equation x ^ 2 + y ^ 2 = 9 passes through the two focuses and two vertices of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, then the circle is inscribed to the ellipse
c^2 = a^2 - b^2
Then C = b = 3
a = 3√2
The length of major axis is 2A = 6 √ 2

It is known that the ellipse C1: x ^ 2 / b ^ 2 + y ^ 2 / A ^ 2 = 1 (a > b > 0) has a certain point of a (3,0), the focus f (0, c) (c > 0) passing through C1 and the chord length of the vertical major axis is 18 / 5
1) The equation of finding ellipse C1

B = 3
So, x ^ 2 / 9 + y ^ 2 / A ^ 2 = 1
Because the chord length of the vertical major axis is 18 / 5 after (0, c)
So, when y = C, x = 9 / 5
So, x ^ 2 / 9 + C ^ 2 / A ^ 2 = 1
Because, a ^ 2 = B ^ 2 + C ^ 2 = 9 + C ^ 2
So, the simultaneous solution is a = 5
So, x ^ 2 / 9 + y ^ 2 / 25 = 1

If the focus of hyperbola x2 / 9-y2 / N = 1 is on the X axis and the focal length is 10, what is the value of real number n?

N=(10/2)^2-9=16