a. Together, the focus and the directrix determine the parabola. For example, can you visualize the parabola formed by the focus and directrix shown at right? Trace the point and line on your paper and sketch the parabola.
3
b. What is the relationship between the points on the parabola and its focus and directrix? Carefully sketch the parabola that formed on your tracing paper from problem 12‑37. Mark a point on the parabola and label it P. Notice the segment between F and P, and compare it to the segment that is perpendicular to the directrix l and goes to P. What do you notice? Does this relationship seem to hold for all points on the parabola? Explain.
4
HINT: The RED Point F is the focus of the parabola. Move it up and down to see how the distance between the focus and directrix affects the shape of the parabola.
5
c. How does the distance between the focus (the point) and the directrix (the line) affect the shape of the parabola?
6
7
powered by
powered by
New Blank Graph
Examples
Lines: Slope Intercept Form
example
Lines: Point Slope Form
example
Lines: Two Point Form
example
Parabolas: Standard Form
example
Parabolas: Vertex Form
example
Parabolas: Standard Form + Tangent
example
Trigonometry: Period and Amplitude
example
Trigonometry: Phase
example
Trigonometry: Wave Interference
example
Trigonometry: Unit Circle
example
Conic Sections: Circle
example
Conic Sections: Parabola and Focus
example
Conic Sections: Ellipse with Foci
example
Conic Sections: Hyperbola
example
Polar: Rose
example
Polar: Logarithmic Spiral
example
Polar: Limacon
example
Polar: Conic Sections
example
Parametric: Introduction
example
Parametric: Cycloid
example
Transformations: Translating a Function
example
Transformations: Scaling a Function
example
Transformations: Inverse of a Function
example
Statistics: Linear Regression
example
Statistics: Anscombe's Quartet
example
Statistics: 4th Order Polynomial
example
Lists: Family of sin Curves
example
Lists: Curve Stitching
example
Lists: Plotting a List of Points
example
Calculus: Derivatives
example
Calculus: Secant Line
example
Calculus: Tangent Line
example
Calculus: Taylor Expansion of sin(x)
example
Calculus: Integrals
example
Calculus: Integral with adjustable bounds
example
Calculus: Fundamental Theorem of Calculus
example
Terms of Service|Privacy Policy