mps said:What does it mean when one says that "A circle and an ellipse with a focus at the circle’s
center can touch each other only at the longer axis"?
Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways?
Thanks! :)
mps said:hi Yukoel,
no, i don't seek a mathematical proof. i just want to understand the statement. I still don't really understand... what do you mean by it "states constraint of the tangency condition"?
thanks for your help!
So you mean the end of the ellipse closer to the other focii?Yukoel said:... the point of contact has to be the end of longer axis of ellipse.I think this is what it means.
mps said:So you mean the end of the ellipse closer to the other focii?
A circle is a shape with all points equidistant from the center. An ellipse is a shape with two focal points and the sum of the distances from any point on the ellipse to the two focal points is constant.
The intersection of a circle and an ellipse is the set of points that lie on both shapes.
Yes, a circle and an ellipse can intersect. The intersection can occur at one point, two points, or in rare cases, no points.
Yes, it is possible for a circle and an ellipse to intersect at only one point. This occurs when the circle is tangent to the ellipse at one point.
To make a circle and an ellipse touch, the radius of the circle can be adjusted so that it is equal to the distance from the center of the ellipse to the nearest point on the circle. This will result in the two shapes touching at one point.