# Search Results for “tangent”

##### Maximum Area Triangle

The app uses a physical model to find the largest area triangle whose vertices lie on a smooth closed curve (defined by the red control points). The triangle defined by the tangent lines at the vertices is displayed, along with its medians. What do you notice about the maximum?##### Rotating Ellipses

Two ellipses rotate within a third such that the two smaller ellipses are always tangent to each other and the larger ellipse. Adjusting the variable X demonstrates this rotation. All three ellipses are constrained only by their implicit equations, and the moving ellipses' equations include functions of X that allow them to rotate. Can you figure out what the equations are (the other constants in the equations are a, b, h, and k)?##### Basic Derivatives

Drag the point to see how the slope of the line relates to the**x**value of the point at which it’s tangent to the function. Can you figure out what the function is, based on the values of the

**x**and

**y**coordinates? The slope of the line can also be represented in terms of

**x**; can you figure out what this representation is? This representation is the derivative

*of the entire function*, not just at a single point. This is called the derivative of the function, and can be notated by, for example, the derivative of

**F(x)**=

**F’(x)**, although there are many other notations as well.