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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Differentiating and Integrating the Formula for Area of Circle [05/11/1998]

The formula for a circle's circumference is the derivative of the formula for its area. What is the significance of this?

Distance from Point to Ellipse [05/19/1997]

How do you find the minimum distance from a point to an ellipse when the point can be either inside or outside the ellipse?

Distance of Chord from Circumference [12/31/1997]

Is it possible to calculate the vertical distance, at a right angle, from a chord to the circumference of a circle?

Distance to Mars [07/25/1997]

What is the distance from Earth to Mars?

Dividing a Circle using Six Lines [08/29/2001]

What is the largest number of regions into which you can divide a circle using six lines?

Do Circles Have Corners? [08/06/1999]

Can you have angles or corners without edges?

Donkey Grazing Half a Field [08/08/1997]

A donkey is attached by a rope to a point on the perimeter of a circular field. How long should the rope be so that the donkey can graze exactly half the field?

Drawing a Circle Tangent to an Angle [05/13/2000]

Given an angle and any point inside it not on its bisector, how can you draw a circle that goes through the point and is tangent to both sides of the angle with just a compass and protractor?

Drawing An Ellipse [11/24/1997]

How do you draw an ellipse with only a straight edge and a compass?

Drawing or Constructing an Ellipse or Oval [02/22/2006]

I know you can draw an ellipse using a string and two tacks. How do I determine the length of the string and the location of the tacks to draw an ellipse of a particular size?

Earth's Curvature [07/07/2003]

How far would you have to 'walk' in no gravity to get 1 foot off the ground?

Earth's Rotational Speed [07/25/1999]

If you were standing at the equator at sea level, how fast would you be travelling in relation to the center of the earth?

Ellipse Area and Circumference [04/19/2001]

How can I draw an ellipse and find the area and circumference?

Ellipse Bounding A Rectangle [7/15/1996]

How do I calculate the ellipse bounding any given rectangle?

Ellipse Equation [03/11/1999]

How do I get the equation of an ellipse, given four points and the inclination of the major axis?

Ellipse Geometry [08/09/1998]

I wish to draw a line departing at a given angle from the long axis of an ellipse and bisecting the perimeter of the ellipse at right angles to the tangent at that point...

An Ellipse Or A Circle? - Parametric Equations [12/05/1998]

Is this parametric equation elliptical or a circle?... And how do I compute the slopes at points 0, pi/4, pi/2, 3pi/2,and 2pi?

Ellipses: Pythagorean Relationship [2/12/1996]

In an ellipse with major axis of 2a, minor axis of 2b, and foci c (on the major axis), the relationship c squared = a squared - b squared holds true... how do the three numbers fit into a Pythagorean relationship?

Elliptical Orbits in the Solar System [05/22/2005]

I want to have my students draw a scale model of the solar system that shows the orbits of the planets. Assuming I have the apogee and perigee of each planet's orbit about the sun, they need to construct 9 ellipses with some degree of accuracy. What's the best way to go about this?

Endpoint of an Arc [06/25/2001]

Given the center of the circle, the angle of the arc, the radius of the circle, and the starting point of the arc, determine the end point of the arc using cartesian coordinates.

Equation for an Arch [09/09/1997]

I am trying to draw an arch that will go in the ceiling of a building. The arch will be at a maximum height of 28 inches...

Equation of a Circle [05/13/2003]

Find the equation of a circle with the center at point (3, -4) and radius 2.

Equation of a Parabola [12/20/2001]

Given several points that appear to be a parabola, how do you approximate the equation that would give a similar graph?

Equilateral Shapes Inscribed in a Circle [04/07/2003]

Is there a general formula for the length of a side of an equilateral shape that is inscribed in a circle?

Escaping the Tiger [07/10/2003]

A man stands in the center of a circle. On the circumference is a tiger that can only move around the circle. The tiger can run four times as fast as the man. How can the man escape the circle without being eaten by the tiger?

Euclidean Formula for Orthogonal Circles [04/11/2001]

When considering the case when circle C has center at the origin and radius 1, we need to show that the equation of the circle orthogonal to circle C and with center (h,k) is given by: x^2-2hx+y^2-2ky+1=0.

An Euler Circle Proof [03/26/1999]

I'm having trouble with the incenter and the inradius.

Find Circle Center and Radius [09/21/2001]

Given three sets of (x,y) coordinates that lie on the circumference of a circle, how do you find the center and radius of the circle?

Finding a Parabola [2/5/1996]

Find the equation of the parabola that is one unit away from X^2 at all points.

Finding a Point on a Circle [5/28/1996]

How do I find the y1 value?

Finding Miles Per Hour [03/06/2002]

If a wheel is making 64.2 revolutions per minute, how many miles per hour is it going?

Finding Quadratic Roots Geometrically or Graphically [12/07/2004]

How do you find the roots of a quadratic function geometrically? For example, what is the algorithm to find roots for f(x) = x^2 + 1 by looking at the graph?

Finding Radius Given Arc Length and Chord to Arc Height [08/28/2005]

I'm purchasing a curved piece of glass for some furniture. The curve (arc) is 60 inches long. The height (the midpoint of the chord to the center of the arc) is 11 inches. I need to know the radius of this curve so the glass company can make my glass. Any thoughts?

Finding Radius Given the Length of a Chord [04/09/2006]

Two points on a circle are 78 units apart and the distance from the circle to the center of the chord connecting them is 12 units. How do I calculate the radius?

Finding the Area of an Arc [1/23/1996]

When you draw a circle and make a chord from one point to another, how would you find the area of that arc (formula)?

Finding the Axes of an Ellipse from a Known Cone [01/26/2001]

I'm trying to solve a specific situation regarding lighting when viewed as an oblique circular cone...

Finding the Center of a Circle [06/06/1999]

How can I find the center and radius of a circle that is in the form: Ax^2 + Cy^2 + Dx + Ey + F = 0?

Finding the Center of a Circle [5/29/1996]

How can you find the center of a circle using a ruler and compass?

Finding the Center of a Circle from 2 Points and Radius [01/24/1997]

Given two points on a circle and the circle's radius, find the center coordinates of the circle.

Finding the Center of a Circle from 2 Points [06/01/1999]

How do you find the centre of a circle if you are given 2 points on the circle and the radius?

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