![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
If the focus of the ellipse x ^ 2 / 25 + y ^ 2 / M = 1 is on the x-axis and the ratio of the focal length to the length of the major axis is 1:3, then M
The focus is on the X axis
So m
If the focal length of the ellipse with focus on X axis X ^ 2 / M + y ^ 2 / 4 = 1 is equal to 2, then M =? Find the specific process,
The focus is on the X axis
m=a²,4=b²
c²=m-4
The focal length is 2C = 2
c=1
So m = 5
Given that the focus of the ellipse X & # 178; + KY & # 178; = 1 is on the x-axis, and the length of the major axis is three times that of the minor axis, then the value of the real number k is
x²+ky²=1
x²+y²/(1/k)=1
The focus is on the X axis
Then a = 1, B = 1 / √ K
The length of the long axis is three times that of the short axis
That is, 2A = 3 * (2b)
a=3b
That is, 1 = 3 / √ K
So k = 9
If the line y-kx-1 = 0 and the ellipse x ^ 2 / 5 + y ^ 2 / M = 1 have a common point, then the range of M is?
No, the answer is - 1 to 1 or negative root 2
Combination of number and shape: straight line passing through point (0,1)
1. If M 〉 = 1, the point (0,1) is in the ellipse, so there is always an intersection. But let x ^ 2 / 5 + y ^ 2 / M = 1 be an ellipse, so m! = 5, so m belongs to [1,5] and (5, positive infinity)
2. If M0, let the equation have a unique solution, then 5K ^ 2 = 1-m > 0, then M
RELATED INFORMATIONS
- 1. If the two vertices of the ellipse x2a2 + y2b2 = 1 (a > b > 0) are a (a, 0), B (0, b), and the left focus is f, △ fab is a right triangle with angle B as the right angle, then the eccentricity e of the ellipse is () A. 3-12B. 1+54C. 5-12D. 3+14
- 2. Application of inverse proportion function in mathematics of grade two The grain depot needs to store 600 tons of corn from the drying field 1. What is the functional relationship between the time t (unit: day) and the speed V (unit: ton / day)? 2. There are 40 employees in the grain depot, and the maximum daily storage capacity is 0.5 tons per person. It is expected that the corn storage can be completed in a few days at the earliest? 3. After 25 days of continuous work, the weather forecast says that it is likely to rain in the next few days. The grain depot decides to put all the remaining corn into the warehouse the next day. How many more people are needed to help complete the task?
- 3. If the distance between the vertex and the origin of the image of quadratic function y = AX2 + BX + C is 5, then C =?
- 4. Given the triangle ABC, a [4,0], the absolute value BC = 2, BC moves on the y-axis, then the trajectory equation of the outer center P of △ ABC is
- 5. In the plane rectangular coordinate system, given o (0,0) a (1,0) B (1,1) C (0,2), if any three of the four oabc points are selected, the probability of forming a right triangle is 0
- 6. In the plane rectangular coordinate system, a (3, - 4), B (2, - 1), C (x, 2) if points a, B, C can form a triangle, then what conditions should x satisfy
- 7. When Beibei calculates 1.6 plus a two place decimal, he aligns the ends of the two numbers and gets the sum of 3.49. Write the correct formula
- 8. The approximate value of a two place decimal that is rounded to one place is 6.8, and the maximum value of the two place decimal is 0______ The smallest is______ ．
- 9. What is the ratio of 1 to 8 / 1 to 0.6
- 10. The ratio of 8:25 to 2:3 becomes the simplest integer ratio (). The ratio of this ratio is () (detailed process) Do you have anything more detailed? First floor, I don't understand
- 11. If the two focal points of the ellipse x ^ 2 / 25 + y ^ 2 / 9 = 1 are F1 and F2 respectively, and point P is any point on the ellipse, find the perimeter of pf1f2?
- 12. The left and right focal points of the ellipse x2a2 + y2b2 = 1 (a > b > 0) are F1 and F2 respectively. The intersection of the straight line with an inclination angle of 120 ° through F2 and the ellipse is m. if MF1 is perpendicular to the X axis, the eccentricity of the ellipse is () A. 12−2311B. 2-3C. 2（2-3）D. 33
- 13. The center is at the origin, the focus is on the y-axis, and the focal length is (3,0) Such as the title
- 14. It is known that the center of the ellipse with eccentricity of 4 / 5 is at the origin and the focus is on the x-axis It is known that the center of the ellipse with eccentricity of 4 / 5 is at the origin and the focus is on the x-axis. The hyperbola takes the major axis of the ellipse as the real axis and the minor axis as the imaginary axis. If the focal length of the hyperbola is 2 root sign 34, the equations of the ellipse and hyperbola can be solved
- 15. It is known that the center of the ellipse is at the origin, the focus is on the y-axis, the focal length is 4, and the eccentricity is 2 / 3. Suppose that the focus of the ellipse on the positive half axis of the y-axis is m, and a and B are on the ellipse And the vector AB = 2, the vector MB, find the linear equation where the line AB is
- 16. Let the center of the ellipse be at the origin o, the focus be on the x-axis, the eccentricity be √ 2 / 2, and the sum of the distances between a point P and two focus points on the ellipse be equal to √ 6. Let the center of the ellipse be at the origin o, the focus be on the x-axis, the eccentricity be √ 2 / 2, and the sum of the distances between a point P and two focus points on the ellipse be equal to √ 6. (1) if the straight line x + y + M = 0 intersects the ellipse at two points a and B, and OA ⊥ ob, find the value of M?
- 17. Given that K is a real number, if the focal length of hyperbola X2K − 5 + Y22 − | K | = 1 has nothing to do with the value of K, then the value range of K is () A. （-2，0]B. （-2，0）∪（0，2）C. [0，2）D. [-1，0）∪（0，2]
- 18. Some problems on the standard equation of hyperbola 1. The focal coordinates are (0, - 6), (0,6) and (2, - 5) respectively 2. Eccentricity e = 4 / 3, imaginary axis length is 2 times root 7, focus on Y axis 3. The focal length is 10, the distance between two vertices is 6, and the vertex is on the X axis
- 19. The coordinates of the focus are (- 6,0), (6,0) and the standard equation of hyperbola passing through point a (- 5,2)
- 20. It is known that the center of the hyperbola is at the origin, the focal points F 1 and F 2 are on the coordinate axis, the eccentricity is 2 ^ 1 / 2 and passes through the point (4, - 10 ^ 1 / 2) It is known that the center of the hyperbola is at the origin, the focus F 1 and F 2 are on the coordinate axis, the eccentricity is 2 ^ 1 / 2 and passes through the point (4, - 10 ^ 1 / 2). Find the hyperbolic equation; if the point m (3, M) is on the hyperbola, find out: the point m is on the circle with the diameter of F 1F 2; find out the area of the triangle f 1m F 2