![](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>)
A problem of rotation equation in advanced mathematics, The curve 4x ^ 2-9x ^ 2 = 36 on the oxy plane, the equation obtained by rotating around the X axis and Y axis, please write in detail,
If it is rotated around the X axis, then x does not change;
Y becomes √ (y ^ 2 + Z ^ 2)
This rotation is
4x^2-9(y^2+z^2)=36.
Similarly, the equation obtained by rotating around the y-axis, y remains unchanged; X becomes √ (x ^ 2 + Z ^ 2)
Then 4 (x ^ 2 + Z ^ 2) - 9y ^ 2 = 36
Finding the surface equation of curve X = 2Z, y = 1 rotating around Z axis
As shown in the figure below
The equation of the surface of revolution of the curve z = 0, y = e ^ x on the xoy plane
Z = 0, y = e ^ x is the curve obtained by the intersection of cylindrical y = e ^ X and xoy plane
One revolution around the X axis gives y = e ^ (± sqrt (x ^ 2 + Z ^ 2))
The equation of the surface of revolution of the curve X ^ 2-4y ^ 2 = 9 on the xoy plane
Let a point (x0, Y0) on the curve rotate around the Y axis and become (x, y, z), then: x0 ^ 2 - 4y0 ^ 2 = 9
If you rotate around the Y axis, there are: x ^ 2 + Z ^ 2 = x0 ^ 2, y = Y0
X ^ 2 + Z ^ 2 - 4Y ^ 2 = 9
How to solve the equation of the surface of revolution generated by the rotation of the curve C: Z square = 5x, y = 0 and X axis for one circle?
z^2=5x,Y=0
The surface equation is y ^ 2 + Z ^ 2 = 2x
The method is as follows
Let f (x, z) = 0, y = 0
The surface equation of revolution generated by one revolution around the X axis is
F (x, positive and negative sqrt (y ^ 2 + Z ^ 2)) = 0
The equation of the surface of revolution generated by one revolution around the z-axis is
F (positive and negative sqrt (y ^ 2 + Z ^ 2), z = 0
Rotation around which axis, which variable in the equation will remain unchanged, and the other variable is replaced by the sum of the squares of the remaining two variables, and then square, plus a sign before the root. Sqrt (x) means square root of X
Parametric equation of curved surface obtained by curve y = cos (x) rotating around X axis
y^2+z^2=(cosx)^2
The formation parameter equation is x = U
y=cosucosv
z=cosusinv
Find the equation of the surface of rotation of the curve X ^ 2 + Z ^ 2 = 3, y = 1 around the Y axis
Such as the title
There is something wrong with the title. Please correct it!
x^2+z^2=3
y=1
It's a circle, the y-axis is perpendicular to the plane it's on, it's not a surface
The surface x ^ 2-2y ^ 2 + Z = 2 is the equation of the surface of revolution formed by the curve cut by the xoy plane rotating around the Y axis
I already know the answer. I hope to have a detailed explanation
By solving the simultaneous equations x ^ 2-2y ^ 2 + Z = 2 and z = 0, the curve equation x ^ 2-2y ^ 2 = 2 on xoy surface can be obtained. Then let x = (+ or -) (x ^ 2 + Z ^ 2) ^ (1 / 2), and then solve the equation x ^ 2 + Z ^ 2-2y ^ 2 = 2
The asymptote equation of hyperbola 4x ^ 2-9y ^ 2 = 1 is?
Right. It should be. Y = + - (B / a) x A is 1 / 9, B is 1 / 4
Application of multiple integral of high number to find s-area of surface
S is the part of cone x ^ 2 + y ^ 2 = 16 / 9z ^ 2 cut by cylinder (X-2) ^ 2 + y ^ 2 = 4
RELATED INFORMATIONS
- 1. Higher mathematics problem: how to calculate the surface area of the ball by the integral of the circumference? Sphere surface area s = 4 * Pai * r * r How to use it Circumference C = 2 * Pai * r Integral? Is it S=2∏＊∫0 R∫0 ∏/2 r* sinθ dr * dθ =4∏R2 ? (for format problem, superscript and subscript are inseparable, ∫ is the integral sign, ∫ 0 R means the product from 0 to R)
- 2. Figure area enclosed by curve and straight line The area enclosed by the curve y = x ^ 3 + 1, the straight line x + y = 3 and two coordinates
- 3. In a semicircle, draw a maximum right triangle with the center point o as the right vertex. It is known that the area of the triangle is 25 square meters. How about the area of the circle?
- 4. Through the point P (- 2, - 3), make two tangents of the circle C: (x-4) ^ 2 + (Y-2) ^ 2 = 9, the tangent points are a ` B respectively. Find the square of the circle passing through the center C and the tangent point is A.B
- 5. Q.2 analytic geometry straight line and circle, hope to answer as soon as possible, 1. It is known that a circle centered on point C (T, 2 / T) (t ∈ R, t ≠ 0) intersects with X-axis at point O and point a, and intersects with Y-axis at point O and point B, where point O is the origin of rectangular coordinate system. Let y = - 2X + 4 intersect with circle C at point m, N, and if om = on, find the equation of circle C 2. Let the image of the quadratic function f (x) = x & # 178; + 2x + B (x ∈ R) have three intersections with the two coordinate axes in the plane rectangular coordinate system xoy, and the circle passing through the three intersections is marked as C (1) I have worked out the value range of B
- 6. How to prove the symmetry theorem of double integral This theorem is very good, but I want to know the principle, which is the process of proving this theorem
- 7. Using polar coordinates to calculate double integral ∫ [D] (6-3x-2y) DXDY =? Where D: x ^ 2 + y ^ 2
- 8. The equation for the projection of line L on the plane Π: x + y + 2z-5 = 0 is obtained
- 9. What is the value of the real number a if the length of the line X-Y = 2 cut by the circle (x-a) & sup2; + Y & sup2; = 4 is the root 2
- 10. A polar coordinate transformation problem R = sin θ, what does its rectangular coordinate equation look like? In definite integral. This is the upper limit of integral
- 11. For a cube wood block with 10 cm edge length, dig a small cube with 2 cm edge length in the center of front and back, left and right, upper and lower sides respectively, and calculate the surface area of the block
- 12. Half of the square metal block with a side length of 10 cm is placed on a plane with an area of 1 square meter. When the indication of the spring dynamometer is 10 N, the pressure is 4 times 10 cubic PA, and the density of the metal block is calculated G is 10N / kg, the answer is 5 * 10 ^ 3kg / m ^ 3
- 13. Find the maximum area and perimeter of inscribed rectangle of ellipse x 2 / a 2 + y 2 / B 2 = 1 (a > b > 0)
- 14. Given the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, find the maximum area of its inscribed rectangle
- 15. If a straight line passing through the center of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 intersects the ellipse at two points a and B, and F is a focal point of the ellipse, what is the maximum area of △ ABF Such as the title Why are a and B symmetrical about o. Not quite understand
- 16. A vertex on the major axis of the ellipse x2 + 4y2 = 4 is a. take a as the right vertex to make an isosceles right triangle inscribed on the ellipse. The area of the triangle is______ ．
- 17. Given the inscribed rectangle ABCD of the ellipse x2 / A2 + Y2 / B2 = 1 (a > b > 0) (ABCD is all on the ellipse), find the maximum face of the rectangle
- 18. The inscribed rectangle of ellipse A & # 178; / X & # 178; + B & # 178; / Y & # 178; = 1 has all fixed points on the ellipse. What is the maximum area of the rectangle?
- 19. The line passing through a focal point of ellipse 2x & # 178; + Y & # 178; = 2 intersects the ellipse at two points P and Q to find the maximum area of △ poq?
- 20. It is known that the center of the ellipse C is at the origin, the focus is on the x-axis, one of its vertices is (0,1), and the eccentricity is equal to 2 / 5 of the original number 5 (1) Please write down the specific process!