All Questions
10
questions
3
votes
2
answers
230
views
An unexpectedly difficult geometry problem
I've run into a geometry problem that feels like it should have an easy answer. But short of numerical integration, I can't find a way to solve it.
Consider a filled circle on top of a filled ellipse ...
- 169
0
votes
1
answer
117
views
Analytical solution for ratio of circle to ellipse area
I am interested in finding an analytical solution for the ratio of the area of a circle within an ellipse to the area of an ellipse.
so the ratio of the magenta area to that of the magenta + cyan area....
- 115
3
votes
2
answers
184
views
Area of a circle which is interior to the parabola
I'm trying to solve the following problem:
Find the area of the circle $x^2+y^2=8$, which is interior to the
parabola $y^2=2x$.
I have my own solution and I want to verify whether it is correct. ...
- 147
2
votes
1
answer
937
views
Maximize the area of an ellipse inscribed in a semicircle.
An ellipse inscribed in semi-circle touches the circular arc at two distinct points and also touches the bounding diameter its major axis is parallel to the bounding diameter. When the ellipse has the ...
- 19.3k
0
votes
3
answers
96
views
What is the meaning of exterior here and how to find the solution? [closed]
Find the area of the circle $x^2+y^2=16$ which is exterior to the parabola $y^2=6x$ using definite integral.
My attempt-
I have solved two to find intersection point $(2,\sqrt{12})$.
But when its ...
user404716
0
votes
1
answer
29
views
Spaces relations
I have a physics question for which I need to determine the radius of a circle.
Given are two Ellipse shapes with the same center (0,0 in a Cartesian space). the Height and Width of the smaller is 1[...
- 113
2
votes
2
answers
267
views
Minimum Area of An Ellipse Surrounding Four Circles
The circles are all four combinations of $(x\pm60)^2+(y\pm25)^2=5^2$ (see pic at end).
The ellipse I've got is one I found via trial and error but there must be an analytical way to solve this, right?...
- 41
2
votes
3
answers
2k
views
Same perimeter and area for a circle and an ellipse
For a given circle, is there exist an ellipse with same perimeter and area as to that circle?
If not, that is my suspicion, is in three-dimension parallel question: For a given sphere, is there ...
- 6,800
1
vote
1
answer
155
views
Area of an ellipse proportional to integral of cross-ellipse distances?
I am curious if the area of an ellipse can be shown to be proportional to the integral of all cross-ellipse distances. Before I define cross-ellipse distance, I will give a motivating example from a ...
- 190
1
vote
2
answers
2k
views
Area of circle formed when sphere is sliced by a plane
First off, when a sphere is cut by a plane, is a circle always formed or does a ellipse get formed in some cases? If a circle is always formed, how do you prove it?
Next, how would you find the area ...
- 4,198