It is known that the hyperbola C1 and the ellipse C2: x ^ 2 / 49 + y ^ 2 / 36 = 1 have a common focus, and the hyperbola C1 passes through M (3 √ 3,2 √ 2), Then the equation of hyperbola C1 is

It is known that the hyperbola C1 and the ellipse C2: x ^ 2 / 49 + y ^ 2 / 36 = 1 have a common focus, and the hyperbola C1 passes through M (3 √ 3,2 √ 2), Then the equation of hyperbola C1 is

First, find out that the focus of the ellipse is (root 13,0) and another is (- root 13,0). This is the focus of the hyperbola. In the hyperbola, if the maximum C is 13, then a ^ 2 + B ^ 2 = 13. This is the first equation
Let the common focus of ellipse x ^ 2 / 2 + y ^ 2 / M = 1 and hyperbola y ^ 2 / 3-x ^ 2 = 1 be f1.f2
P is the intersection of the two curves, then the value of | Pf1 | x | PF2 | is equal to?
Analysis:
From the hyperbolic equation y & # 178 / 3 - X & # 178; = 1, we know that the common focus of ellipse and hyperbola is on the y-axis
Then: m-2 = 3 + 1
The solution is m = 6
Therefore, we can see that the length of the major axis of the ellipse is two root sign 6, and the length of the real axis of the hyperbola is two root sign 3
And point P is the intersection of the two curves. Let | Pf1 | > | PF2|
From the definitions of ellipse and hyperbola, we can get the following results
|Pf1 | + | PF2 | = 2 root number 6, | Pf1 | - | PF2 | = 2 root number 3
It is easy to understand that | Pf1 | = radical 6 + radical 3, and | PF2 | = radical 6 - radical 3
So: | Pf1 | ×| PF2 | = (radical 6 + radical 3) × (radical 6 - radical 3) = 3
Mathematical problem: let the common focus of ellipse x ^ 2 / 6 + y ^ 2 / 2 = 1 and hyperbola (x ^ 2 / 3) - y ^ 2 = 1 be F1 and F2 respectively
1. Let the common focus of ellipse x ^ 2 / 6 + y ^ 2 / 2 = 1 and hyperbola (x ^ 2 / 3) - y ^ 2 = 1 be F1, F2 and P respectively,
Then cos ∠ f1pf2 is equal to (b)
A,1/4 B,1/3 C,2/3 D,-1/3
2. It is known that the distance from a point m on the hyperbola x ^ 2 / 25-y ^ 2 / 24 = 1 to the right focus f is 11, n is the midpoint of MF, and O is the origin of the coordinate,
Then | no | is equal to (b)
A. 11 / 2 B, 21 / 2 C, 1 / 2 D, 1 / 2 or 21 / 2
3. It is known that the curve y ^ 2 = ax has two different intersections A and B with the curve symmetrical about point (1,1). If the line passing through the two intersections
If the inclination angle of a is 45 degrees, then the value of a is (c)
A,1 B,3/2 C,2 D,3
4. If real numbers x and y satisfy x ^ 2 + 4Y ^ 2 = 4, then the product of the maximum and minimum of T = (x-1) ^ 2 + y ^ 2 is____ 6_______
5. Given the points a (2,0), B (4,0), the moving point P is on the line y ^ 2 = - 4x,
The coordinates of the point P that makes the vector AP * vector BP minimum____ (0,0)______
6. Given the points a (3,2), f (2,0), find a point P on the hyperbola x ^ 2-y ^ 2 / 3 = 1, and its coordinates are____ √21/3,2____ When,
|AP | + | PF | / 2 is the minimum
It's better to analyze it
Let the common focus of ellipse X & sup2 / 6 + Y & sup2 / 2 = 1 and X & sup2 / 3-y & sup2; = 1 be F1 and F2 respectively. P is an intersection of two curves, then the value of COS angle f1pf2 is? The half focus of ellipse C = √ (6-2) = 2, the half focus of parabola C = √ (3 + 1) = 2, so they have the same focus F1 (- 2,0), F2 (2,0). X & su
I really flatter you. That's OK. You're a junior or a sophomore. You've long forgotten...
You didn't ask a lot
Derivation of time delay formula in special relativity
The Pythagorean theorem is used in the derivation of the formula. Will these geometric theorems hold at high speed? Will these formulas be modified at high speed?
Can you be more detailed, just say a few words, I'm not very sorry
High speed motion should not be modified, Pythagorean theorem is right, Pythagorean theorem is not applicable, is the expansion of time, space distortion and so on. = = = = = = look at the integral to say two more sentences. Don't think I said less, copy and paste is also meaningless, right? First of all, Pythagorean theorem must be right, because it is mathematics, mathematics is based on abstract theory
In △ ABC, A.B.C is the opposite side of angle A.B.C, M = (2a-c, b), n = (COSC, CoSb), and M / / n. (1) find the size of angle B
Then (2a-c) / b = COSC / CoSb according to the sine theorem (2sina sinc) / SINB = COSC / CoSb 2sinacosb = coscsinb + sinccosb = Sina CoSb = 1 / 2, so B = 60 degree
It is known that the sequence {an} is an arithmetic sequence with the first term of 2. A1, A2 and A4 are equal ratio sequences. The general term formula of the sequence {an} is obtained
a2=a1+d
a4=a1+3d
a2^2=a1a4
a2^2=(a1+d)^2=a1^2+2a1d+d^2
a1a4=a1(a1+3d)=a1^2+3a1d
a1^2+2a1d+d^2=a1^2+3a1d
a1=d=2
an=a1+(n-1)d=2+2(n-1)=2n
a2^2=a1*a4
a2=a1+d=2+d
a4=a1+3d=2+3d
Just insert it
Solution
D = 0 or D = 2
So an = 2
Or an = 2n
The known sequence {an} is an arithmetic sequence with the first term of 2
an=2+(n-1)d
A1, A2, A4 are equal ratio sequence
(a2)^2=a1a4
(2+d)^2=2(2+3d)
D = 2 or D = 0
An = 2n or an = 2
It is known that A1 = 2,
Then the general formula is an = 2 + (n-1) * D
So A2 = 2 + D, A4 = 3D
And because A1, A2 and A4 are equal ratio sequence, A1 * A4 = the square of A2
The solution is d = 2
So the general formula is an = 2 + 2 * (n-1)
How about four questions on page 45 and nine questions on page 46 in volume two of seventh grade mathematics textbook
PEP seventh grade volume 2 mathematics
The resulting figure looks like the letter W
Page 46 question 9: the picture is as follows
How to deduce the clock slow effect formula of special relativity?
.
Let s system be the intrinsic reference system. In S system, there is a time difference δ T, i.e. a (x1, ict1), B (X2, ICT2). In s' system, the time difference is the difference of coordinates in ICT 'component, i.e. clock slow. In coordinates, the situation of time axis and space axis is very similar, but "ruler" is the longest in the intrinsic system, and "clock" is the fastest in the intrinsic system
In △ ABC, ABC corresponds to edge ABC, and (2a-c) CoSb = B COSC, let m = (Sina, 1) vector n = (3, cos2a),
In △ ABC, ABC corresponds to edge ABC, and (2a-c) CoSb = B COSC, let vector M = (Sina, 1) vector n = (3, cos2a), find the value range of vector m times vector n
From (2a-c) CoSb = bcosc, 2sinacosb sinccosb = sinbcosc,
2sinAcosB=sin（B+C）=sinA
cosB=1/2
B=π/3,0
It is known that the sequence {an} is an equal ratio sequence and A1, A2, A4 are equal difference sequence to find the common ratio of the sequence {an}
It is known that the sequence {an} is an equal ratio sequence, and A1, A2, A4 are equal difference sequence. Find the common ratio of the sequence {an}
Hope to tell me how to do % >
A1, A2, A4 form arithmetic sequence
So 2A2 = a1 + A4
The {an} is an equal ratio sequence
a2=a1q
a4=a1q^3
therefore
2×a1q=a1+a1q^3
That is: Q ^ 3-2q + 1 = 0
(q-1)(q^2+q-1)=0
Q = 1 or q = (- 1 - √ 5) / 2 or q = (- 1 + √ 5) / 2
Common ratio 1 or (- 1 - √ 5) / 2 or (- 1 + √ 5) / 2 of sequence {an}