Twelfth graders explore the four conic sections — circle, ellipse, parabola, and hyperbola — the elegant curves formed by slicing a cone, each with its own equation and real-world applications from orbits to headlights.
Students will be able to…
Slice a cone at different angles and you get a circle, an ellipse, a parabola, or a hyperbola. These four curves appear everywhere — in orbits, dishes, and bridges. What are they?
Project this and tap each conic section. Have students learn how slicing a cone creates circles, ellipses, parabolas, and hyperbolas!
Tap any phase to open the teacher moves and student actions.
Slice a cone at different angles — what curves appear?
Teacher models.
Class uses the Conics Explorer.
Students identify.
One conic.
Aligned to the Common Core State Standards for Mathematics (High School · Precalculus).
Derive the equation of a circle given center and radius.
Derive the equation of a parabola given a focus and directrix.
Derive the equations of ellipses and hyperbolas.
Solve systems involving a linear and a quadratic equation.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students explore how the foci and eccentricity of an ellipse determine how “stretched” it is. A printable conics sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.