Resources tagged with: Cartesian equations of circles

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Broad Topics > Coordinates, Functions and Graphs > Cartesian equations of circles

Baby Circle

Age 16 to 18
Challenge Level

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Orthogonal Circle

Age 16 to 18
Challenge Level

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Square Pair Circles

Age 16 to 18
Challenge Level

Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.

Rational Round

Age 16 to 18
Challenge Level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Ellipses

Age 14 to 18
Challenge Level

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

Curved Square

Age 16 to 18
Challenge Level

Can you find the area of the central part of this shape? Can you do it in more than one way?