It is known that a focal point of an ellipse is f (1,1), the corresponding collimator is x + y-4 = 0, and the eccentricity is √ 2 / 2

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• 1. If the eccentricity of the ellipse is 12, a focal point is f (3,0) and the corresponding guide line is X-1 = 0, then the elliptic equation is______ ．
• 2. Given that the Quasilinear of the ellipse is x = 4, the corresponding focal coordinate is (2,0), and the eccentricity is 1 / 2, then the equation of the ellipse is?
• 3. The center and focus of an ellipse are o (0,0) and f (4,0) respectively, and the major half axis is 5 Want a detailed process The answer is x ^ 2 / 25 + y ^ 2 / 9 = 1
• 4. The focus of ellipse is on x-axis, the length of short axis is 2 √ 2, the eccentricity is 3 / 6, and the intersection of positive half axis of ellipse and x-axis and y-axis is a B
• 5. Suppose that the center of the ellipse is at the origin o, the focus is on the X axis, the eccentricity is (√ 2) / 2, and the sum of the distances from one point P to two focuses on the ellipse is 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?
• 6. 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
• 7. 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, It is known that the sum of the distances from a point on the ellipse with the focus on the x-axis and the center on the origin to the two focuses is 4. If the root of the eccentricity of the ellipse is 3 / 2, then the equation of the ellipse is
• 8. 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 focal length of the hyperbola with the major axis of the ellipse as the real axis and the minor axis as the imaginary axis is 2 √ 34 (1) Solving the equation of ellipse and hyperbola (2) Let the left and right vertices of the ellipse be a and B respectively, take a point P on the hyperbola in the second quadrant, connect BP intersection ellipse to point m, connect PA and extend the intersection ellipse to point n. if BM (vector) = MP (vector), calculate the area of the quadrilateral anbm
• 9. It is known that the line L: y = x, the ellipse C center is at the origin, the focus is on the x-axis, the focal length is 2, and the short axis length is 2 √ 3 (1) The left focus of ellipse C is F1, the right vertex is B, and the parallel line L 'of straight line L passing through point F1. If l' intersects ellipse C with m and N, calculate the area of triangle MNB
• 10. The original price of a kind of camera is 574 yuan, which has been reduced by 3 / 9. Now the price of the camera is? Yuan, and the car runs 60 km per minute on a section of road Two fifths of the length. How long is this highway In the first day and the second day, 80 parts were finished, and in the third day, 2 / 9 of these parts were finished. How many parts are there in this batch The original price of one kind of camera is 574 yuan. After the price has been reduced by 3 / 9, the current price is? Yuan A section of road, the car 45 branches of 60 kilometers per minute, this section of road is two fifths of the length, how long is this section of road In the first day and the second day, 80 parts were finished, and in the third day, 2 / 9 of these parts were finished. How many parts are there in this batch
• 11. Given hyperbola X & # 178; - Y & # 178; = 4, straight line L: y = K (x-1), try to determine the value range of real number k, so that (1) The line L and hyperbola have two common points (2) Line L and hyperbola have and only have one common point (3) There is no common point between line L and hyperbola
• 12. The equation x2-m of 3-m + Y2 of 2 = 1 represents hyperbola, then the value range of M
• 13. Let the equation x2 / M-1 + Y2 / M + 3 = 1 denote hyperbola and find the value range of M one m-1>0,m+3>0, The solution is m > 1, M > - 3 The range of M is m > - 3 two (m-1)(m+3) Note that hyperbola is not ellipse. Explain the reasons and reasons for your choice
• 14. An example of hyperbola and its standard equation Examples are: When a shell explodes somewhere, the time of the explosion sound heard at a is 2 s later than that at B. It is known that the distance between AB and ab is 800 m and the sound velocity is 340 m / s. The equation of the explosion point curve is obtained (let the explosion point be p (x, y); establish a rectangular coordinate system so that AB is on the X axis, and point O coincides with the midpoint of line AB) In the process of solving the problem, there is one step "Because pa - Pb = 340 * 2 = 680 > 0, x > 0" I can't figure out why "pa - Pb = 340 * 2 = 680 > 0" can lead to "x > 0", and why to determine whether x is greater than 0?
• 15. It is known that there are two intersections between a straight line passing through the right focus of hyperbola x2a2-y2b2 = 1 (a > 0, b > 0) and the right branch of hyperbola with an inclination angle of 45 degrees, then the value range of eccentricity e of hyperbola is______ ．
• 16. Given that the hyperbola and the square of ellipse X / 9 + the square of ellipse Y / 25 = 1 are in common focus, the sum of their eccentricities is 7 / 5, the hyperbolic equation is solved I'm sorry, but the difference between their eccentricities is 7 / 5
• 17. Proposition p: "the equation x2 + y2m = 1 is an ellipse with focus on the y-axis", proposition q: "the function f (x) = 43x3-2mx2 + (4m-3) x-m increases monotonically on (- ∞, + ∞)". If P ∧ Q & nbsp; is a false proposition and P ∨ Q is a true proposition, the range of M is obtained
• 18. To solve the hyperbolic equation with the vertex and focus of the ellipse as the focus and vertex respectively Urgent need process, thank you
• 19. : hyperbolic center in the origin, the focus on the X axis, through the point (2, - 3) and asymptote is y = positive and negative two-thirds x, autumn hyperbolic equation
• 20. The focus is (0,6) (0, - 6), and the hyperbolic standard equation is obtained through the point (2, - 5)