Explore lines, conic sections, parametric curves, and polar coordinates with visual explanations and interactive graphs.
Linear equations in different forms — slope, intercepts, and point-slope.
y = mx + b
The slope-intercept form is the most intuitive way to write a line. m is the slope, b is the y-intercept.
y − y₁ = m(x − x₁)
Point-slope form is perfect when you know a point and the slope, but not the y-intercept.
Ax + By = C
Standard form is useful for finding x- and y-intercepts quickly, and for systems of equations.
Parabolas, ellipses, and hyperbolas — the classic conic sections.
(x−h)² = 4p(y−k)
A parabola is the set of points equidistant from a focus and a directrix.
x²/a² + y²/b² = 1
An ellipse is the set of points where the sum of distances to two foci is constant.
x²/a² − y²/b² = 1
A hyperbola is the set of points where the difference of distances to two foci is constant.
Curves defined by separate x(t) and y(t) functions — time as a parameter.
x = r·cos t, y = r·sin t
A circle can be described parametrically using cosine and sine of an angle parameter t.
x = a·cos t, y = b·sin t
An ellipse uses different scaling factors a and b for the x and y coordinates.
x = r(t − sin t), y = r(1 − cos t)
A cycloid is the path traced by a point on a rolling circle — the brachistochrone curve.
Curves defined by radius as a function of angle — roses, spirals, and cardioids.
Explore conics, parametric curves, and polar coordinates with the interactive visualizer.
Open Analytic Geometry Visualizer