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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.
Çözümlü örnek · x^2 + y^2 - 25
Adım adım
- x^{2} + y^{2} - 25
An expression in x, y. Here is what it does.
Cevabı göster
Şimdi sen Bir problem seçin, ya da kendi probleminizi yazın ya da çizin. Her adım, bir resim, cevap sorulana kadar gizli.
Burada kullanılan sembolleri
Tüm tanım, resim ve her harfin anlamı için herhangi bir sembolü tıklayın.
Nasıl: Conic sections
- An expression in x, y. Here is what it does.
Sık sorulan sorular
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.
More in Precalculus
Complex numbersPolynomial functionsRational functionsSequences and seriesThe binomial theoremVectorsExponential and logarithmic functionsPolynomial division and the remainder theoremParametric equations and polar coordinates