It is known that the length of the minor axis of the ellipse e is 6, and the distance from the focus f to one end of the major axis is 9, then the eccentricity of the ellipse e is equal to () A. 35B. 45C. 513D. 1213

It is known that the length of the minor axis of the ellipse e is 6, and the distance from the focus f to one end of the major axis is 9, then the eccentricity of the ellipse e is equal to () A. 35B. 45C. 513D. 1213

According to the meaning of the question, we can see that B = 3A − C = 9A2 − B2 = C2 or B = 3A + C = 9A2 − B2 = C2, the solution is a = 5, B = 3, C = 4, ∧ e = CA = 45, so we choose B

It is known that the length of the minor axis of the ellipse e is 6, and the distance from the focus f to one end of the major axis is 9, then the eccentricity of the ellipse e is equal to ()
A. 35B. 45C. 513D. 1213

According to the meaning of the question, we can see that B = 3A − C = 9A2 − B2 = C2 or B = 3A + C = 9A2 − B2 = C2, the solution is a = 5, B = 3, C = 4, ∧ e = CA = 45, so we choose B

The distance from a focal point of the ellipse to the corresponding guide line is 4 / 5, and the eccentricity is 2 / 3

Let the elliptic equation be: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, (a > b > 0),
If the right focus is F2 (C, 0), then the right collimator equation is: x = A / E = 3A / 2,
3a/2-c=4/5,
3/2-c/a=4/(5a),
3/2-e=4/(5a),
3/2-2/3=4/(5a),
25a=24,
a=24/25,
e=c/a,
2/3=c/(24/25),
c=16/25,
b=√（a^2-c^2)=8√5/25.
2b=16√5/25.
The minor axis of the ellipse is 16 √ 5 / 25