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Browse High School Conic Sections, Circles
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
About ellipses.
Find the center of a circle.
Is a circle a polygon?
Volume of a tank.
Why is a circle 360 degrees?
 Inscribed Angle Theorem [01/21/1999]

Can you help me prove that an angle inscribed on the same arc as a
central angle is equal to one half that central angle?
 Inscribing a Regular Pentagon within a Circle [04/15/1999]

What are the reasons for the steps in inscribing a regular pentagon
within a circle with only the help of a compass and a straightedge?
 Inscribing a Square within a HalfCircle [04/05/2002]

Is there a way to inscribe a square within a given halfcircle?
 Intersecting Circles [05/13/1999]

A common tangent touches two intersecting circles at S and T. Show that
the line AB bisects the common tangent ST.
 Intersection of Circles [01/16/2002]

Given two intersecting circles, find the coordinates of the intersection
point(s).
 An Introduction to Parabolas [02/04/1999]

What is a parabola? What are some of its properties? What are some
examples of parabolas in real life?
 An Introduction to Pi and Its Use in Circle Problems [04/28/2004]

The doctor helps a confused student with circle parts, their relation
to each other, and pi.
 Involute of a Circle [01/22/1999]

What is the formula for the involute of a circle?
 Irregularly Inscribing a Circle ... of What Radius? [12/24/2011]

A student struggles to determine the radius of a circle given the sidelengths of an
inscribed irregular polygon. First, Doctor Greenie offers a numerical approach; then,
Doctor Floor follows up with the desired analytical method, applying Ptolemy's theorem
and the rational root theorem to a key insight: the radius of the circumcircle remains
invariant under a reordering of the polygon's sidelengths.
 Is a Circle a Polygon? [03/07/1999]

A circle is not a polygon.
 Lateral Surface of a Cone [02/10/1999]

How do you find the formula for the lateral surface of a right cone?
 Latus Rectum [08/08/2002]

I'm trying to find the definition, an explanation, a formula, or
anything that will help me to better understand what latus rectum is.
 Line and Unit Circle; Pythagorean Triples [04/16/2001]

If (X,Y) is a point in the 1st quadrant on the unit circle and m is the
slope of the line passing through (X,Y) and the point (0,1), how can I
express the coordinates (X,Y) in terms of m? Can this be used to generate
Pythagorean triples?
 Line Tangent to an Ellipse [03/29/2003]

Find the equation of the tangent to the ellipse x^2 + y^2 = 76 at each
of the given points: (8,2),(7,3),(1,5). Write your answers in the
form y = mx + b.
 Line Tangent to Two Circles [07/01/1999]

How do you construct a line tangent to two differentsized circles?
 Locus of the Midpoint of a Chord [03/13/1998]

Show that the locus of the midpoint of the chord is a hyperbola.
 Longitude Degrees at the Equator [09/09/1997]

What is the distance in miles between degrees of longitude at the
equator?
 Mathematics and Intuition [07/10/2001]

Certain "puzzlers" in mathematical recreations defy our sense of
experience, leaving you wondering if the answer to a problem can really
be true. How to convince the intelligent nonbeliever?
 Maximum Surface Area [07/03/2003]

Within a rectangle x by y, I wish to draw a shape that is no more than
x across in any direction, but which has the largest possible surface
area within the confines of the rectangle.
 Meaning of Value of b in Hyperbola Equation [05/06/2007]

I have been unable to find a justification for why a^2 + b^2 = c^2 in
a hyperbola. You can justify a^2 = b^2 + c^2 in an ellipse by looking
at special points. Is there a comparable explanation for hyperbolas?
 Minimum Distance from a Point to a Line [7/10/1995]

Find all the values of b such that the minimum distance from the point
(2,0) to the line y = 4/3x+b is 5.
 Missile Launch Code [08/03/2003]

What kind of information could you give all 10 people such that if any
3 of them were to get together, they would be able to launch the
missiles, but if there were only 2 of them, the information would be
insufficient to figure out the code?
 Mixtilinear Incircle Proof [12/11/2000]

In triangle ABC, AB = AC. A circle is tangent internally to the
circumcircle of triangle ABC and also to sides AB and AC at points P and
Q, respectively. How can I prove that the midpoint of the segment PQ is
the center of the mixtilinear incircle of triangle ABC?
 Mutually Tangent Circles [05/22/2000]

Circles A, B and C are mutually tangent and each is tangent to line DFE
at points D, F and E respectively. What is the radius of C as a function
of the radii of A and B?
 NonAlgebraic Explanation of a Parabola [05/16/2000]

What does a parabola look like? How is it formed?
 One More Point Than a Line [07/05/1998]

In terms of 11 correspondence, why does a circle have one more point
than a line?
 The Origin of Conic Sections [10/02/1998]

What are the origins of conic sections?
 Origin of Radians [05/27/2002]

Where, exactly, did radians come from?
 Overlapping Circles [07/14/1999]

Each of two overlapping circles has a radius of 6 inches. How long is the
darkened portion, in inches?
 Painting a MerryGoRound [06/06/2002]

You have two concentric circles. A chord of the larger, which
measures 70 feet, is tangent to the smaller. What is the area of the
region between the circles?
 Parabola [06/06/2001]

What is the meaning of the word parabola?
 Parabola Given Three Points [03/27/2002]

How can I find the equation for a parabola given three points on it?
 Parabola: Proving Parallel Rays [05/21/2003]

Given only the geometric definition of a parabola (all points equally
distant from focus and directrix), provide a simple geometric proof
that all rays emanating from the focus reflect from the parabola
parallel to the axis of symmetry.
 Parabolas, b/2a ? [03/13/2002]

I've thought about why the form b/2a works when trying to graph a
parabola, but I just cannot figure it out.
 Parabolas in Everyday Life [05/18/2001]

What types of things have been made using parabola shapes?
 Parabolas Through Pairs of Points [07/13/2002]

Can infinitely many parabolas pass through any two points in a plane?
 Parabolic Equation of an Arch [05/25/1998]

Finding the equation of the parabola in the McDonald's golden arches.
 Parabolic Golf Shot Equations [01/24/2002]

Does the ball reach the green?
 Pascal's Theorem [10/07/1998]

Can you explain Pascal's Theorem? How does it relate to conic sections?
 Perimeter of an Ellipse [06/29/1999]

Is there a formula that gives the exact perimeter of an ellipse?
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