# Search Results for “fermat-point”

##### Polar Point Ellipse

The polar point of a line in an ellipse is a common point to the chords defined by the common tangents through the points on the line. Play with it and the meaning will be clear! (Go to**Full Screen**if the green points won't drag)

##### Point Trilateration

Use any three points and their distances from a fourth point to locate the fourth point.##### Polar Point Parabola

The polar point of a line in a parabola is a common point to the chords defined by the common tangents through the points on the line. (Go to**Full Screen**if the green points won’t drag)

##### parabola envelope

We use a trick to let the trace "open up" as you drag a point. The trick is this: an initial point is given parametric location s*t, create a tangent at this point and its envelope as s varies. Now hide the original point and create another point with parameter t, and make it draggable. Dragging the new point changes the value of t and we see a trace from 0 to t.##### Projectile High Point

Press the play button to fire a projectile in the direction of the arrow. Move the arrow and try again. Notice the high points of the trajectory lie on an ellipse. If the initial velocity of the projectile is v, and gravity is g, what is the equation of the ellipse?##### 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.