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High School Archive

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?

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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 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: (x-3)^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: Newton-Raphson 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 non-overlapping 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 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 mutually-tangent 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?

Difference between Oval and Ellipse [10/18/2001]

What is the difference between an oval and an ellipse? Am I right if I say that "all ellipses are ovals, but all ovals cannot be ellipses"?

Difference in Radius, Difference in Speed [06/25/2002]

What is the difference in speed between a point on the tread of a tire and another point closer to the center, if the tire is rotating at 5000 rpm?

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