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If the focus of parabola y ^ 2 = 4x is f and the guide line is l, what is the number of circles passing through points F, m (4,4) and tangent to l
The center of the circle is on the vertical line of FM, and the point above (x, y) satisfies that the distance to f is equal to the distance to the collimator. List out two equations and judge how many values X of the quadratic function has. According to the actual situation, let's see how many are there. If I'm not wrong, it's one, either one or two~
A mathematical problem about parabola!
Given parabola y = x & sup2; - ax + 2 (A-3)
1. It is proved that no matter what the value of a is, there are two intersections between this parabola and the x-axis
2. When the vertex position of the parabola is the highest, find the distance between the two intersections of the parabola and the X axis
(1) It is proved that: ∵ △ = (- a) ^ 2-4 × 1 × 2 (A-3) = a ^ 2-8a + 24 = (A-4) ^ 2 + 8 > 0 ∵ no matter what the value of a is, there are always two intersections between this parabola and the x-axis. (2) y = x ^ 2-ax + 2 (A-3), the opening of the parabola is upward, the ordinate of the vertex of the parabola = - [(A-4) ^ 2 + 8] / 4, when a = 4, the vertex coordinates of the parabola
A mathematical problem (about parabola)
Let P1 and P2 be parabola, y = X2, and the equation of L is y = - x + 3?
Let P1 (x1, X1 ^ 2), P2 (X2, X2 ^ 2), where x1
Solving quadratic equation
The side length of a square is 2cm. Subtract four triangles from the four corners of the square to get an octagon
Finding the side length of an octagon
RELATED INFORMATIONS
- 1. How to define a quadratic equation with at most one positive root
- 2. Quadratic equation KX ^ 2 + 2 (K + 1) x - (3K-1) = 0 if the sum of two elements in the equation is equal to the product, the value of K can be obtained
- 3. The vertex coordinates of the parabola y = 2 (x-3) 2 + 1 are () A. （3，1）B. （3，-1）C. （-3，1）D. （-3，-1）
- 4. Through a focus F of ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1 (a > b > 0), make a chord perpendicular to the major axis. What is the chord length?
- 5. Chord length problem of elliptic focus Derivation of focus chord formula
- 6. What is the minimum distance between a point on the ellipse and the focus? Where is the point? What is the minimum distance to the point on the focus ellipse? Where is the point? If you know, tell me,
- 7. It is known that the hyperbola (X & # 178; / 4) - (Y & # 178; / 8) = 1, the two ends a and B of the chord passing through the left focus F1 are on the left branch, and | ab | = 6, F2 is the right focus, find the perimeter of △ abf2
- 8. In hyperbola C: X & # 178; / A & # 178; - Y & # 178; / B & # 178; = 1, the chord length perpendicular to the real axis through the focus is 2 √ 3 / 3 The distance from the focus to an asymptote is 1, find C
- 9. The chord length formula of the straight line section ellipse should be proved in detail and deduced step by step~
- 10. Conic In the plane rectangular coordinate system, there are two fixed points F1 (0, radical 3) F2 (0, - radical 3). If the moving point m satisfies MF1 + MF2 = 4 Let the line L: y = KX + T intersect the curve with two points a and B, and let the line L1: y = K1X intersect at point D. if K × K1 = - 4, it is proved that D is the midpoint of ab
- 11. Let the intersection points of the parabola y = 4-x ^ 2 and the straight line y = 3x be a and B. point P moves from a to B on the arc of the parabola, 1. Find the coordinates (a, b) of point P to maximize the area of triangle PAB 2. Prove that the figure enclosed by parabola y = 4-x ^ 2 and straight line y = 3x is divided into two parts with equal area by straight line x = a
- 12. If the vertex of parabola y = x & # 178; + 4 is p, and the two intersections of parabola y and X are C and D, then the area of triangle PCD is_________
- 13. The volume formula of ellipse
- 14. For the calculation of ellipse perimeter and arc height on both sides, detailed calculation formula is required, The sole is 40 long and 18 wide The bottom is 36 in length and 14.5 in width Height 12
- 15. Arc area formula
- 16. A simple physics problem (particle motion) At the same position above the ground, two small balls are thrown upward at the initial velocity of V1V2. After the second ball is thrown, it meets the first ball in t time. By changing the time interval between the two balls, the T value can be changed. Let V1V2 be selected and V1 be selected
- 17. When two passengers get off the train, they follow the same route to the same place where the station is s. The speed of passenger a is V1 in the first half of the time and V2 in the other half. Passenger B uses V1 to complete the first half of the journey and V2 to complete the second half. If it takes T1 and T2 for passenger a and passenger B to arrive at the same place from the station, then T1 =? T2 =?
- 18. A physical problem in sports One elevator, with acceleration of 2 when starting, with acceleration of - 1 when braking, and building height of 52m The elevator first speeds up, then rises at a constant speed, and finally decelerates at a constant speed. What is the maximum speed of 16 seconds when the elevator is used in the whole process?
- 19. In the experiment, how to determine whether the trajectory is a parabola is studied
- 20. Is the trajectory of horizontal throwing a parabola! Is the trajectory of horizontal projectile a parabola? But its trajectory is only half of that of parabola (quadratic function with opening downward)?