Ask Dr. Math

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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Solve for Radius [09/09/1997]

Given a circle through three points, what is the equation for the intersection of the perpendicular bisectors?

Square Inscribed in a Circle [09/28/1997]

What percent of the circle is contained within the square?

Square Peg, Round Peg [08/22/1997]

Which fits better, a square peg in a round hole, or a round peg in a square hole?

Squares and Circles: How Many Intersections? [02/27/2002]

What is the largest possible number of times a square can intersect a circle when the square is placed on top?

Straight Lines and Conic Sections [10/14/2008]

Is a pair of intersecting straight lines a conic section? If so, what is its eccentricity value?

Strange Points of Locus [6/6/1996]

Given two fixed points, A and B, on a plane, if P is a moving point such that PA and PB are perpendicular and the locus of P is a circle, should we exclude points A and B?

Symmetry Lines [03/30/2000]

How many symmetry lines are in a circle?

Tangent Circle Construction [12/02/1996]

Given a circle with two points inside it, construct another circle that passes through the given points and is tangent to the given circle.

Tangent Common to Two Ellipses [10/24/2002]

I have two general ellipses in space and I want to find the equation of the tangent common to these ellipses.

Tangent Line and Circles [04/05/1999]

Two circles of different radius are tangent to each other. A line is drawn tangent to both circles. How long is the segment between the two points of tangency of the line and the circles?

Tangents to Circles [06/25/1999]

How can I prove that a line L is tangent to Circle C if and only if L is perpendicular to ZA, where Z is the center C and A is a point on C?

Tangent to Parabola [10/21/1996]

What is the slope of the lines tangent to the parabola y = x^2 that pass through the point (2,1)?

Theorem of the Broken Chord [12/14/2001]

Prove the theorem of the broken chord (if AB and BC make up a broken chord in a circle, where BC is greater than AB, and if M is the midpoint of arc ABC, the foot F of the perpendicular from M on BC is the midpoint of the broken chord).

Three Intersecting Circles [07/14/1999]

Two circles (X^2+Y^2+4X-4Y-8 = 0 and X^2+Y^2-X-Y-2 = 0) intersect at points P and Q. Another circle (3X^2+3Y^2-13X+KY+L = 0) passes through P, Q, and A (3,1). What is L?

Three Ways to Find the Vertex of a Parabola [02/19/2007]

For H(x) = -x2 - 8x - 15, what are the coordinates of the vertex, what is the equation of the axis of symmetry, and what is the greatest value of the function?

Traceable Mathematical Curves [10/27/1997]

Is there any way to tell just by looking if a curve is traceable or not? Is there some property of a curve that will tell you this? Do curves have formulas?

Tracing an Ellipse [08/17/1997]

How do you form an ellipse using 3 points?

Trisecting a Circle with Parallel Cuts [06/12/2002]

Can two parallel cuts divide a circle into three parts of equal size?

Trisecting a Pizza [05/13/2002]

Without the use of a ruler, protractor or other measuring device, is there a simple way to divide a pizza into 3 equal sized slices?

Two Circles, Four Tangents, Collinear Midpoints [12/20/1998]

Given two circles that do not touch there are four distinct tangents common to both circles. Prove that the midpoints of the tangents are collinear.

Two-column Proof [5/24/1996]

Theorem: tangent segments from a point outside a circle to a circle have equal lengths.

Two-Column Proof: Parallel Tangents [03/08/2002]

Prove that tangents to a circle at the endpoints of a diameter are parallel.

Two Discs, One Rotating [7/5/1996]

Two circular discs have radii 8 cm and 28 cm. The larger disc is fixed while the smaller disc rolls around the outside of the larger...

Two Problems on Tangents [07/09/1998]

How can you show that the arc and the angle formed by two tangents are supplementary? Find the radius of circle O, given the following...

Types of Cones [01/19/1999]

Does a cone have an edge? Does it depend on what type of cone you have? What are the different types of cones?

Uses of Conics [05/09/1999]

What are some real life examples of conics?

Uses of Ellipses [04/02/2003]

Where are ellipses found in real life?

Ways to Remember the Meaning of Circumference, Radius, Diameter, and Chord [03/18/2004]

If the minute hand touched the edge of the clock, would it be most like a diameter, radius, circumference, or chord of a circle? I have a hard time remembering what each of those means.

What is the Area Not Shared by the Circles? [3/3/1995]

Two circles intersect such that their centers and their points of intersection form a square with each side equal to 3. What is the total area of the sections of the square that are not shared by both circles?

What is the Circumference of the Reservoir? [04/09/2003]

John and Tina start running around a round reservoir in opposite directions, meeting for the first time after John has traveled 100 yards, and again 60 yards before Tina has completed her first lap.

Where Will the Runners Meet? [03/29/1999]

Two runners, A and B, start 90 degrees away from each other on a circular track and run at the same speed. If Runner B decides to cut across the track, where will they meet?

Which Quadrant in the Unit Circle? [11/30/1998]

Find the quadrant in which C(s) is located. Example: C(14pi/3)= C(2pi/ 3). Thus, C(14pi/3) is in quadrant II.

Who uses Ellipses? [12/3/1995]

I need to find out someone (or some occupation) that uses ellipses in their work.

Why 6.28 Radians? [10/07/1998]

Why is a circle divided into approximately 6.28 radians?

Why are Manhole Covers Round? [05/09/2000]

Why are most manhole covers round? Why aren't manhole covers on the streets squares or rectangles?

Why Are There 2Pi Radians in a Circle? [11/24/2003]

Why are there two pi radians in a circle? I know that it has something to do with the formula for the circumference of the circle, but I'm not sure how it works.

Why Is a Circle 360 Degrees? [07/01/1998]

Why is a circle defined as 360 degrees?

Why is Area of a Circle Equal to Pi * (Radius Squared)? [07/05/2005]

I know the formula for the area of a circle is A = pi*r^2, but why does that give the area?

Why is Pi a Constant? [08/01/2000]

Why is the circumference of a circle divided by the diameter, or pi, the same number for every circle?

Why Pi? [07/19/2002]

Instead of using pi, why don't we measure the radius and circumference of a given circle, and use that ratio to find the area? Wouldn't that be more accurate?

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