Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Equations of circles
Interpret and construct coordinate equations of circles
Problem types
- Select the true statements about a circle from its equation
- Equations of circles
- Center and radius from the general form of a circle
Builds on
- Completing the square
- Distance in the coordinate plane
- Why every circle is similar to every other · Useful idea
Every circle is a dilation of the unit circle, so x squared + y squared = r squared is the unit circle scaled by r.
- A tangent from a point outside a circle · Useful idea
The tangent at a point of a circle is perpendicular to the radius to that point, so its slope is the negative reciprocal of the radius slope.
- The incircle and the circumcircle · Useful idea
The circle through three points has its center where the perpendicular bisectors meet, and its equation uses that center and radius.
Leads to
Related skills
- The complex plane · Related idea
The equation of a circle x squared + y squared = r squared is the set of complex numbers with modulus r.
- Polar and Cartesian coordinates · Related idea
A circle centered at the origin has polar equation r = constant.
- Perimeter and area from coordinates · Shared foundations
- Proofs that use coordinates · Shared foundations
- A parabola as points equally far from a focus and a line · Shared foundations
Open the interactive map to explore lessons and skill connections.