randRange(-5, 5) randRange(-5, 5) randRange(1, 5) H === 0 ? "x^2" : expr(["^", ["+", "x", -H], 2]) K === 0 ? "y^2" : expr(["^", ["+", "y", -K], 2])

Graph the circle expr(["+", X2T, Y2T]) = R * R.


graphInit({ range: 11, scale: 20, axisArrows: "<->", tickStep: 1, labelStep: 1, gridOpacity: 0.05, axisOpacity: 0.2, tickOpacity: 0.4, labelOpacity: 0.5 }); label( [ 0, 11 ], "y", "above" ); label( [ 11, 0 ], "x", "right" ); addMouseLayer(); graph.circle = addCircleGraph();
Drag the center point and perimeter of the circle to graph the equation.
[ graph.circle.center[0], graph.circle.center[1], graph.circle.radius]
if (_.isEqual(guess, [0, 0, 2])) { return ""; } return _.isEqual(guess, [H, K, R]);
graph.circle.setCenter(guess[0], guess[1]); graph.circle.setRadius(guess[2]);

The equation of a circle with center (\blue{h}, \green{k}) and radius \pink{r} is (x - \blue{h})^2 + (y - \green{k})^2 = \pink{r}^2.

We can rewrite the given equation as (x - \blue{negParens(H)})^2 + (y - \green{negParens(K)})^2 = \pink{R}^2.

Thus, the center of the circle should be (\blue{H}, \green{K}) and the radius should be \pink{R}.

circle([H, K], R, { stroke: PURPLE, strokeWidth: 1, strokeDasharray: "- " }).toBack();