Given that the eccentricity of ellipse y ^ 2 / A ^ 2 + x ^ 2 / b ^ 2 = 1 (a > b > 0) is 3 / 5, and the distance between two focal points is 3, the value of a + B is obtained

Given that the eccentricity of ellipse y ^ 2 / A ^ 2 + x ^ 2 / b ^ 2 = 1 (a > b > 0) is 3 / 5, and the distance between two focal points is 3, the value of a + B is obtained

Centrifugation e = C / a = 3 / 5,
2c=3
The solution is C = 3 / 2
a=5/2
So B & # 178; = A & # 178; - C & # 178; = 25 / 4-9 / 4 = 4
So B = 2
So a + B = 5 / 2 + 2 = 9 / 2

Given that the sum of the distances from a point on the ellipse to two focal points (- 2,0), (2,0) is equal to 6, then the minor axis length of the ellipse is?

2A = 6 a = 3 C = 2 b = stem 5

The focus of the ellipse is on the y-axis, the distance ratio between a focus and the two ends of the major axis is 1:4, and the length of the minor axis is 8, then the standard equation of the ellipse is______ ．

Let the equation of ellipse be y2a2 + x2b2 = 1 (a > b > 0), then a − Ca + C = 142b = 8a2 = B2 + C2, the solution is a = 5B = 4, the standard equation of ellipse is y225 + x216 = 1, so the answer is y225 + x216 = 1

If the distance ratio between one focus of the ellipse and the two ends of the major axis is 1:4 and the length of the minor axis is 8, then the standard equation of the ellipse is obtained
There is another problem: given that the hyperbola 4x + y = 64 has a common focus, the root of the ratio of the real axis length to the imaginary axis length of the hyperbola 3: solve the hyperbolic equation

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It is known that the center of the ellipse is at the origin, the focus is on the x-axis, and the length of the major axis is twice that of the minor axis

Let the elliptic equation be x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, a = 2b is obtained from the known, and x ^ 2 / (4B ^ 2) + y ^ 2 / b ^ 2 = 1 can be obtained by substituting x = 2, y = - 6, and 1 / b ^ 2 + 36 / b ^ 2 = 1 can be obtained. The solution is B ^ 2 = 37, so a ^ 2 = 4B ^ 2 = 148, so the elliptic equation is x ^ 2 / 148 + y ^ 2 / 37 = 1

The length ratio of the major axis to the minor axis of the ellipse is 2, and a focus is (2 pieces of 15,0) to solve the standard equation

The length ratio of major axis to minor axis is 2, i.e. a: B = 2, a = 2B
c^2=a^2-b^2=4b^2-b^2=3b^2
C = 2 root sign 15
So, (2 radical 15) ^ 2 = 2B ^ 2 = 60
b^2=30
a^2=4b^2=120
So the elliptic equation is: x ^ 2 / 120 + y ^ 2 / 30 = 1

It is known that the focus of the ellipse is on the x-axis, a: B = 5:3, and the focal length is equal to 16?
Come on, come on

c=16/2=8
Let a & sup2; = B & sup2; + C & sup2; a: B = 5:3
a=10 b=6
So the standard equation of ellipse is: X & sup2 / 100 + Y & sup2 / 36 = 1

What is the difference between the standard elliptic equations with focus on x-axis and y-axis?

What are the differences between the standard elliptic equations with focus on x-axis and y-axis
If the focus is on the x-axis, the major axis is on the x-axis;
If the focus is on the y-axis, the major axis is on the y-axis;
For X & # 178 / / A & # 178; + Y & # 178 / / B & # 178; = 1; (a > 0, b > 0)
If the focus is on the x-axis, then a > B
If the focus is on the y-axis, a < B;
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The standard equation of two ellipses passing through point a (- 1, - 2) and having the same focus as the ellipse X & # 178 / 6 + Y & # 178 / 9 = 1 is

It can be seen that the focus coordinate of the ellipse is (0, ± root 3)
If point a is on the ellipse, the sum of the distances from point a to the two focal points is radical [(- 1) &# 178; + (- 2-radical 3) &# 178;] + radical [(- 1) &# 178; + (- 2 + radical 3) &# 178;] = 2 [radical (2 + radical 3) + radical (2-radical 3)]
Then 2A = 2 [radical (2 + radical 3) + radical (2-radical 3)]
So, if a = radical (2 + radical 3) + radical (2-radical 3), then a & # 178; = 6
Then B & # 178; = A & # 178; - C & # 178; = 6-3 = 3
So the elliptic standard equation is X & # 178 / 3 + Y & # 178 / 6 = 1

If the minor axis of ellipse C is 2, and two vertices on the minor axis and a focal point form an equilateral triangle, what is the standard equation of ellipse C

2b=2
b=1
Because it's an equilateral triangle
c=√3b=√3
a=√(c²+b²)=2
C:x²/4+y²=1
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