The plane at an angle of 30 degrees from the bottom of the cylinder cuts the cylinder to obtain an ellipse and the equation of the circle The radius of the cylinder is 4. The rectangular coordinate system is self built. I can't wait

The plane at an angle of 30 degrees from the bottom of the cylinder cuts the cylinder to obtain an ellipse and the equation of the circle The radius of the cylinder is 4. The rectangular coordinate system is self built. I can't wait

Cylinder bottom diameter d = 2 * 4 = 8
The major axis length of ellipse = D / cos30 ° = 16 √ 3 / 3
Length of minor axis of ellipse = D = 8
So a = 8 √ 3 / 3, B = 4
The standard equation of ellipse is
x²/(64/3)+y²/16=1

The radius of the bottom of the circle is 4, and the plane which is 30 degrees from the bottom of the circle cuts the circle to get an ellipse=

The major axis is: 8 △ cos30 ° = 9.24 (it can be obtained by Pythagorean theorem)
The minor axis is: 8 (the minor axis is the diameter of the circle directly)

Using a plane to cut a cone, the plane obtained can not be 1. Circle 2. Triangle 3. Semi ellipse

Use a plane parallel to the bottom to cut a cone, the plane is 1. Circle
Cut a cone with a plane passing through the vertex and perpendicular to the bottom, and the plane obtained is 2. Triangle
Cut a cone with a plane which is not the vertex but perpendicular to the bottom, and the plane obtained is 3. Semi ellipse
Therefore, there is no solution to this problem

If you use a plane to cut a cylinder, you can't get a rectangle B circle C ellipse D trapezoid

D
Cut perpendicular to the bottom is a
Parallel is B
A little slant is C

If a cylinder is cut by a plane, can the cross section be trapezoid?
If you use a plane to cut a cylinder, what shape is the cross section? Is it trapezoid? I can't figure out how to cut a trapezoid

It could be round, oval, rectangular, square
Triangle, trapezoid:
See Fig

If we can get the section of a square, what is the relationship between the radius of the lower surface and the height of the cylinder

Possible. Take a point on the edge of the upper bottom and any chord at the lower bottom. The figure obtained by cutting the cylinder through the plane of this point and the line where the chord lies is a triangle
h

What shape can a cylinder cut with a plane? A cone?

What kind of figure can a cylinder be cut with a plane? A cone?
If you use a plane to cut a cylinder, you can cut out:
Rectangle, triangle, circle
If you cut a cone with a plane, you can cut out:
A branch of a triangle, circle, ellipse, parabola, or hyperbola
The above cut-out figure
The outline of a figure, such as a circle
It can also be understood as graphic surface, such as round surface

If you cut a cylinder with a plane, you can't get a figure

The landlord's question is not clear, the answer has innumerable
First of all, if you cut a cylinder with a plane, the cross-section figure you get may be circle, ellipse, rectangle, or in special cases, square. As for what the figure can't be, do you understand?!
If the cross section can not be: triangle, Pentagon, hexagon Etc

If one focus and two vertices of an ellipse are three vertices of an equilateral triangle, the length of the major axis of the ellipse is several times longer than that of the minor axis

∵ one focus and two vertices of an ellipse are three vertices of an equilateral triangle, ∵ C = 3b ∵ a = B2 + C2 = 2B ∵ 2a2b = 2

If one focus and two vertices of an ellipse are three vertices of an equilateral triangle, the length of the major axis of the ellipse is several times longer than that of the minor axis

∵ one focus and two vertices of an ellipse are three vertices of an equilateral triangle, ∵ C = 3b ∵ a = B2 + C2 = 2B ∵ 2a2b = 2