zeion said:so x = (3/5)y.
zeion said:Then I sub x back into original equation and get y, I get y = +/- 1/(sqrt(2)), which is wrong.
What did I do wrong?
An ellipse is a geometric shape that resembles a flattened circle. It is defined as the set of all points in a plane whose distances from two fixed points, called foci, add up to a constant value.
To find two points on an ellipse with horizontal tangents, you can use the derivative of the ellipse equation. The points will be located at the intersection of the ellipse and the horizontal line that is tangent to the ellipse at that point.
A tangent is a straight line that touches a curve at a single point. It is perpendicular to the curve at that point and represents the instantaneous rate of change of the curve at that point.
Finding points on an ellipse with horizontal tangents is important in many real-life applications, such as engineering and physics. It allows us to determine the slope of the curve at that point, which can provide valuable information for designing structures or predicting the behavior of moving objects.
Yes, there are two special cases: when the horizontal tangent is located at the center of the ellipse, and when the horizontal tangent is parallel to the major axis of the ellipse. In these cases, the derivative of the ellipse equation will be equal to 0, and the points can be found by substituting this value into the equation.