0
votes
1answer
326 views

Find locus of points relating to an ellipse

I would like to find the equation of the following locus. For a big circle C centered at (0,0), the locus of points that the sum of distances to Y-axis and to C is 1, say in the first quadrant, is ...
4
votes
2answers
246 views

What is a the intuition behind a parametric equation?

I have always used equations for the line (y=a + bx) in R2. Recently I came upon this thing called parametric equations. I cannot grasp the difference between them and the equations for lines that I ...
0
votes
1answer
867 views

Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
1
vote
2answers
243 views

Is there a generalized method of rotation for curves?

I know that we can rotate a curve in $R^2$ about a linear axis, as is common for first year calculus problems involving solids of revolution. But has anyone come up with a general method to take a ...
2
votes
1answer
451 views

Property of an ellipse

I need proof for the following question. Also, I want to know, can we apply the same for other conics. If yes, where and when... Please explain. Show that there exists a point K on the major axis of ...
7
votes
2answers
444 views

The Dido problem with an arclength constraint

It is well known that the solution to the classical Dido problem is a semicircle, and that the solution to the classical isoperimetric problem is a circle. It's also reasonably obvious that the ...
3
votes
1answer
276 views

Curve of a fixed point of a conic compelled to pass through 2 points

Suppose that in the plane a given conic curve is compelled to pass through two fixed points of that plane. What are the curves covered by a fixed point of the conic, its center (for an ellipse), its ...
8
votes
3answers
1k views

Minimal Ellipse Circumscribing A Right Triangle

Find the equation of the ellipse circumscribing a right triangle whose lengths of it's sides are $3,4,5$ and such that its area is the minimum possible one. You may chose the origin and orientation ...