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How to find the locus of the middle point of a line segment whose distance between two points on a conic curve is fixed Take the parabola as an example: Y & # 178; = 2px, (P > 0), a and B are two points on the parabola, and ab = 3, find the trajectory equation of the midpoint m in ab
Can ellipses and hyperbolas do the same?
Chord length of conic
I've seen other people use trigonometric functions to solve the problem. It doesn't take so long. But I forgot to solve the problem again. It's like constructing a trigonometric function with m-square + n-square under the root of the same name
I know the chord length formula is just lazy and I don't want to calculate it
In addition, it seems that the slope of tangent can be calculated by reciprocal
There are three ways to calculate the chord length obtained by the intersection of straight line and conic
1. A quadratic equation with one variable about X is obtained by combining the equations of a straight line and a conic curve, which is calculated by using the chord length formula. | ab | = (1 + K ^ 2 under the root sign) ×| x1-x2 |, where k is the slope of the straight line, and x1 and X2 are the two parts of the equation; (the slope of the straight line must exist in the formula of | ab | = (1 + K ^ 2 under the root sign) ×| x1-x2 |
2. The parameter equation of straight line is used to solve the problem;
3. The geometric meaning of ρ in polar coordinate equation is distance
Some problems about focus chord in conic curve
The focus is on typical examples and related methods, the more complete the better!
Through the fixed point P (0,1) make a straight line L, so that l and the curve y2 = 2x have and only have one common point, such a straight line L has () a.1 B.2 C.3 D.4 2. The straight line passes through the focus of the parabola y2 = 2px (P > 0), and intersects with the parabola at two points a (x1
Quadratic radical
With the sign a, the root sign B, just like this formula A, is it possible to include a positive sign or a negative sign in the formula?
1. (√ 3 + √ 2 - √ 1) (√ 3 - √ 2 + √ 1) speak in detail, I don't understand what you want, don't lose a step!
two
Given √ 25-x-square - √ 15 + x-square = 4, find the value of √ 25-x-square + 15 + x-square! Slow down!
As a result, the original formula of the first problem: the original formula = [[3-3 + (2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1 = 2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1)] [[3 - (3 - (2-2-2-2-2-2-2-2-2-2-2-2-1)] [[[(25-25-x (25-x-x & \35\\\\\\\\\\3535\\\x & # 178;) (15 + X & # 17
As shown in the figure, the circumference of the parallelogram ABCD is 102 cm. When the CD is the bottom, it is 20 cm high; when the BC is the bottom, it is 14 cm high,
What is the area of the parallelogram ABCD?
Let BC = x, then CD = 51-x
According to the meaning of the title
14x=20(51-x)
14x=1020-20x
34x=1020
x=30
So s parallelogram ABCD = 14 * 30 = 420 square centimeter
It is proved that there are infinite positive integers k such that for every prime P, the number P & # 178; + k is a composite number
Because prime number is odd, P & # 178; is also odd, as long as K is odd, P & # 178; + k is even, combined
Considering the special case of P = 2, only k = 5,11,17,21,23,29,31 When, 2 & # 178; + k is a composite number
Since there are innumerable odd numbers n which are composite numbers at the same time, as long as k = n-4, P & # 178; + K must be composite numbers
So K has countless
Elementary school mathematics volume 2 unit 2 cone and cylinder text
Read the math book!
The length of a rectangle is reduced by 4cm, and the rest is a square with a perimeter of 24cm. How many centimeters is the perimeter of the original rectangle? How many square centimeters is the area?
The perimeter of the text is 24 cm, the side length of the square is 24 ／ 4 = 6 (CM), the length of the rectangle is 6 + 4 = 10 (CM), the perimeter of the rectangle is (10 + 6) × 2 = 32 (CM), and the area of the rectangle is 10 × 6 = 60 (square cm)
For a seven digit number, the number in one million is five times that in ten thousand, and the number in one hundred thousand is equal to that in one million
For a seven digit number, the number in one million is five times that in ten thousand. The number in one hundred thousand is equal to the sum of the number in one million and the number in ten thousand. The numbers in other places are all zero. What's the number?
5610000
It takes 24 seconds for a train to pass a 360 meter tunnel and 16 seconds to pass a 220 meter bridge. How about the body length and train speed?
A set of equations: let the length of the car be x meters and the speed be y meters per second
1：（220+x）÷y=16
2：（360+x）÷y=24
The solution is x = 60, y = 17.5
RELATED INFORMATIONS
- 1. The relationship between the slope of focus chord and the ratio of focus chord and eccentricity of conic curve? RT
- 2. Given that a, B, C are real numbers, f (x) = AX2 + BX + C, G (x) = ax + B, when - 1 ≤ x ≤ 1 | f (x) | ≤ 1. (1) prove: | C | ≤ 1; (2) prove: when - 1 ≤ x ≤ 1, | g (x) | ≤ 2; (3) let a > 0, when - 1 ≤ x ≤ 1, the maximum value of G (x) is 2, and find f (x)
- 3. F (x) = log2 [(1-ax) / (x-1)] odd function a is a constant. 1. Find the value of A. 2. Prove that f (x) monotonically decreases in the interval (1, positive infinity), 3.3. If the inequality f (x) B - (1 / 2) ^ x holds for any value of X on [3,5], find the value range of real number B
- 4. How to judge whether a function is even or odd
- 5. What is "odd function. Even function"? We don't have that in our math books, But there are some problems about odd function and even function Please be more specific
- 6. Given that f (x) is an even function, G (x) is an odd function, f (x) + G (x) = x ^ 2 + 2 ^ x, find f (1)
- 7. Let f (x) be a continuous even function on (- ∞, + ∞), and prove that f (x) = ∫ (0 → x) f (T) DT is an odd function
- 8. How to write a function in the form of an odd function and an even function Take F (x) = x + 1 / (2 + x) as an example,
- 9. It is known that the domain of definition of functions f (x) and G (x) is r, where f (x) is odd, G (x) is even, and f (x) + G (x) = 1 / (the square of x-x + 1) Finding the analytic expressions of F (x), G (x)
- 10. It is known that f (x) is an odd function and G (x) is an even function. When x ≥ 0, f (x) = LG (x + 1); when x < 0, G (x) = f (x), the analytic expression of G (x) when x > 0 is obtained
- 11. The midpoint problem of conic chord To solve the linear equation of the chord of hyperbola with a (m, n) as the midpoint, we can use f (x1) - f (x2) to get the result. But why does it not exist?
- 12. F1, F2 are the two focal points of the ellipse X29 + Y27 = 1, a is the point on the ellipse, and ∠ af1f2 = 45 °, then the area of △ af1f2 is___ ．
- 13. What is the area of the triangle f2ab if a straight line passes through the left focus F1 of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 and the line parallel to the Y axis intersects the ellipse and ab? There is another problem: the two foci F1F2 of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, P is the point on the ellipse, if the triangle f1pf2 is a right triangle (angle f1pf2 = 90 degrees), find the area of the triangle f1pf2
- 14. The line L passing through the focus f on the ellipse 2x ^ 2 + y ^ 2 = 2 intersects the ellipse at two points a and B to find the maximum area of Δ AOB (o is the origin) The answer is only √ 2 / 2. Is there anything wrong in it? Or is the answer wrong There's a wrong step in the middle. Oh, forget it
- 15. If the line y = KX intersects the ellipse x ^ 2 / 4 + y ^ 2 = 1 at two points a and B, and ab ≥ √ 10, find the value range of K
- 16. As shown in the figure, the straight line y = kx-1 intersects the x-axis and y-axis at two points B and C respectively, Tan ∠ OCB = 12 (1) Find the coordinates of point B and the value of K; (2) if point a (x, y) is a moving point on the line y = kx-1 in the first quadrant, try to write out the functional relationship between the area s of △ AOB and X when point a moves; (3) explore: under the condition of (2): ① when point a moves to what position, the area of △ AOB is 14; ② if it holds, whether there is a point P on the X axis So that △ POA is an isosceles triangle? If it exists, please write the coordinates of all P points that meet the condition; if not, please explain the reason
- 17. In the plane rectangular coordinate system, the coordinates of point a are (3, - 4), its symmetry about y axis, the coordinates of point B are (), △ OAB are () triangles
- 18. In the plane rectangular coordinate system, B and a are on the X and Y axes respectively, and the coordinate of B is (3,0) ∠ ABO = 30 degree AC bisection ∠ OAB intersects X axis at C (1) Find the coordinates of point C (2) If D is the middle point of AB, ∠ EDF = 60 °, (E on AC, f on BC), it is proved that CE + CF = OC
- 19. 11. It is known that y + 1 is proportional to x, and when x = 3, y = 5, the functional relationship between Y and X is obtained, and the value of a when the point (a, - 2) is on the function image is obtained
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