# Tag Archives: equation of circle

## Tangent Circles

Consider the circles that have radii and are tangent to the line at the point . Find the sum of the coordinates of the centers of the circles. Source: NCTM Mathematics Teacher, August 2006 Solution For the two circles to … Continue reading

## Real Solutions (x,y)

How many real solutions are there that satisfy the two equations and ? Source: NCTM Mathematics Teacher, September 2006 Solution The graph of is a circle centered at the origin and radius = . The graph of is a hyperbola … Continue reading

## Lattice Points

A point with integral coordinates is called a lattice point. For example, is a lattice point, whereas is not. How many lattice points lie on the graph of ? Source: NCTM Mathematics Teacher, January 2006 Solution The graph of is … Continue reading

## Points on Circle

Find all points that have an -coordinate twice the -coordinate and that lie on a circle of radius with center at . Source: NCTM Mathematics Teacher, January 2006 SOLUTION Let for some real number . Equation of circle or or … Continue reading