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Conic sections
Circles, ellipses, parabolas and hyperbolas as equations and as surfaces sliced.
Slice a cone and you get a circle, an ellipse, a parabola or a hyperbola; algebraically they are the second-degree equations in x and y. Completing the square in each variable reveals the centre and shape. The 3D view draws z = the expression, whose level curve z = 0 is the conic.
Voorbeeld van werk · x^2 + y^2 - 25
Stap voor stap
- x^{2} + y^{2} - 25
An expression in x, y. Here is what it does.
Onthul het antwoord
Nu jij. Kies een probleem, type of teken je eigen. Elke stap, een foto, het antwoord verborgen totdat je het vraagt.
Hier gebruikte symbolen
Tik op elk symbool voor de volledige definitie, een afbeelding en wat elke letter erin betekent.
Hoe: Conic sections
- An expression in x, y. Here is what it does.
Vragen die mensen stellen
What is a function, really?
A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.
Why do we need complex numbers?
Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.
Meer in Precalculus
Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates