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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?
 Common Internal Tangent [03/29/2002]

Two circles with radii 9 and 6 are 2 cm. apart. Find the length of the
common internal tangent.
 A Complete Proof about Tangential Circles [06/05/1998]

Can you show me a proof, with full justification, of the following
theorem? Two circles of the same radius touch at A ...
 Complete This Square: x^2 + y^2  6x + 2 = 0 [03/16/2003]

I thought completing the square only involved quadratic functions,
such as f(x) = ax^2 + bx + c = 0. This question relates to the
equation of a circle...
 Completing the Square in a Hyperbola Equation [01/04/2004]

A discussion of how to complete the square and how to apply it to the
equation of a hyperbola such as 4(x^2 – 4x)  9(y^2 + 6y) = 101.
 Conical Vertex? [03/27/2003]

What is the point at the tip of a cone called?
 Conic Sections and Parallel Lines [3/18/1995]

Our teacher told us there was a way to cut a cone with a plane to get
parallel lines. Another teacher in the department can do it
algebraically, but no one can do it physically. Is there such a plane in
reality or only in theory?
 Connection Between Circumference and Surface Area [05/08/1998]

Can you explain the connection between the circumference of a circle and
the surface area of a sphere?
 Constructing an Ellipse [04/15/1997]

How do you draw an ellipse?
 Constructing a Tangent to a Circle [03/19/1999]

Construct a tangent to a circle through a given point not on the circle.
 Constructing a Tangent to a Circle, Continued [03/26/2013]

The proof of a tangency construction leaves a couple puzzled. Doctor Peterson
explains how it relies on a property of angles inscribed in semicircles.
 Constructing Axes of an Ellipse with Straightedge and Compass [01/23/2006]

Presented with the graph of an ellipse, is there a way to determine
the axes by using straightedge and compass?
 Convert Degrees to Radians [7/21/1996]

How do you convert degrees to radians, and vice versa?
 Converting RPM to MPH and MPH to RPM [04/07/2002]

What is the formula for converting RPM's from an 'X' inch diameter
wheel into miles per hour?
 Coordinate Geometry and Distance Formula [10/02/2002]

I need to find the center and radius of the following equations and
then graph them: (x3)^2 + (y+4)^2  9 = 0; x^2 + y^2 = 36.
 Coordinate Geometry of Circles [02/26/2003]

The line with equation y = mx is a tangent to the circle with equation
x^2 + y^2  6x 6y +17 = 0. Find the possible values of m.
 Counting Regions Formed by Chords of a Circle [05/19/1998]

Determining the number of regions formed by connecting n points on the
circumference of a circle.
 Cow Grazing Half the Circle: NewtonRaphson Method [01/18/1998]

Assume a perfect circle filled with grass and a cow tied with a rope to
the fence around it...
 Creating Tangents to Circles [10/24/2007]

I know how to draw a tangent to a circle from a point outside the
circle. How can I create four distinct tangents that are common to two
nonoverlapping circles?
 Cutting a Circle out of a Square [2/14/1996]

What is the area (to the nearest square centimeter) of the largest circle
that can be cut from a square piece of sheet metal 73cm. on each side?
Explain how you determined this.
 Cutting a Wedge out of a Disk to Make a Cone [12/05/2005]

A cone can be formed by cutting a wedge out of a disk and then rolling
the remaining part into the cone shape. How can I determine how big
the wedge should be to make a cone of given dimensions?
 Cyclic Quadrilaterals [8/30/1996]

A cyclic quadrilateral touches a circle at each vertex. What angles do
these points make with the centre of the circle?
 Cycloid [01/30/1998]

What is a cycloid and what does it do?
 Defining an Ellipse, Continued [04/16/2013]

A student wonders why a sum of squares describes ellipses. Doctor Peterson
elaborates on a previous conversation about the general equation, in which he
sketched the system as a loop wrapped around two anchor points.
 Defining a Parabola with Three Points [05/09/2009]

Given three distinct points, one of which is the vertex of a parabola,
is there only one unique parabola that passes through the points?
 Definition of an Ellipse [1/4/1995]

I have a question concerning the concept of an ellipse. It is said that
the equation for an ellipse is Pf + Pr= 2a where P is a point on the
ellipse and f and r are the points of the foci. How do we know that this
is true, that is that Pf + Pr = 2a? How did we come up with the constant
of 2a?
 Deformed Bullet [04/11/2002]

If you initially have a circle and it gets smushed into an ellipse,
how do you determine the diameter of the initial circle, knowing the
major and minor diameter of the ellipse?
 Degenerate Conics [03/04/1998]

Identifying the degenerate cases for the graphs of equations in conic
form.
 Degenerate/Nondegenerate Figure [10/27/2001]

We need to know what a nondegenerate circle is. (We're trying to decide
whether this is a model of incidence geometry, but don't know the
definition.)
 Degrees in a Circle [09/22/1997]

Why does a circle measure 360 degrees  is there a special reason for
this calculation?
 Derivation of the Equation of an Ellipse [06/23/1999]

How can I derive the equation of an ellipse from its definition?
 Deriving the Hyperbola Formula [04/27/1998]

When speaking of hyperbolas, why does C^2 = A^2 + B^2?
 Descartes Circle Theorem [01/15/2008]

What is the radius of the largest circle which can be inscribed within
the area formed by three mutuallytangent circles, in terms of the
radii of the three circles?
 Describe the Locus [03/28/2002]

What is the locus of all points in a plane two inches from a point A?
 Designing and Building a Cone Frustum [03/24/2004]

I need help making making a pattern for a frustum shape to protect a
large piece of equipment. How can I find the distance between the top
and bottom arcs in a straight line?
 Determining Cone's Original Dimensions from a Slice [05/18/1999]

Given the inside and outside arc lengths and the thickness of a truncated
cone, find the inner and outer radii and the angle.
 Determining the Equation of a Circle [05/12/2000]

How can I determine which of five equations describes the set of all
points (x,y) in the coordinate plane that are a distance of 5 from the
point (3,4)?
 Diameter of a Ball [11/25/2001]

A child rolls a ball on a level floor 4.5m to another child. If the ball
makes 15 revolutions, what is its diameter?
 Diameter of a Circle Circumscribed Around a Triangle [05/13/1998]

Applying the Pythagorean Theorem to find the diameter of the circle
circumscribed around a triangle with side lengths 25, 39, and 40.
 Diameter of Flying Saucer [5/27/1996]

We are constructing an oval racetrack in Atlanta...
 Diameter of the Base of a Cone [08/12/1998]

How do you find the formula to calculate the diameter of the base of a
cone of nine degrees at various lengths?
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