Wentworth's Plane and Solid Geometry · Book IX, Exs. 866–884 · Book 10: Book IX: Conic Sections
137. Exercises on the parabola
Goal: Your student proves and constructs several properties of the parabola.
You'll need
- The book, open to these pages
- A ruler (straightedge) and a pair of compasses
- Sharp pencil, eraser and plain paper (or a geometry notebook)
What's in the book
Page 424: Exercises on the parabola, Ex. 866–884.
The lesson, step by step
Warm up
Ask: State three facts about the tangent of a parabola.
Constructions
Ex. 868. To draw a tangent and a normal at a given point of a parabola.
Ex. 869. To draw a tangent to a parabola parallel to a given line.
Ex. 879. Given a parabola, to find the directrix, axis, and focus.
Theorems
Your student picks two:
Ex. 866. If the abscissa of a point is equal to its ordinate, each is equal to the latus rectum.
Ex. 870. The tangents at the ends of the latus rectum meet at D.
Ex. 871. The latus rectum is the shortest focal chord.
A locus
Ex. 880. To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Wrap up
Your student explains one solution aloud.
Answers to the book's problems
Ex. 866: by Prop. II, y² = 4AF × x; if x = y then x = 4AF. Ex. 870: they are tangents at the ends of a focal chord (§ 884). Ex. 880: a parabola with the point as focus and the line as directrix.
Worked out for this site from the scan. If a number in your copy differs, trust the book.