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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.
Esempio svolto · x^2 + y^2 - 25
Passo dopo passo
- x^{2} + y^{2} - 25
An expression in x, y. Here is what it does.
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Simboli utilizzati qui
Toccare qualsiasi simbolo per la definizione completa, un'immagine, e che cosa ogni lettera in esso significa.
Come: Conic sections
- An expression in x, y. Here is what it does.
Domande che la gente chiede
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.
Altro in Precalculus
Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates