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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.
Kushanda muenzaniso · x^2 + y^2 - 25
Step by step
- x^{2} + y^{2} - 25
An expression in x, y. Here is what it does.
Kuratidza mhinduro
Zvino iwe Choose a problem, or type or draw your own. Every step, a picture, the answer hidden until you ask.
Mubhadharo wakasununguka unowedzera mazita ezvidzidzo, zvinyorwa zvezvidzidzo zvawakati wazvigadzirira, zvidzidzo zvawave uchizvigadzirisa, uye mudzidzisi waungabvunza nezvechidzidzo ichi. Maths inowanikwa kune vese, vasiri vadzidzi kana vadzidzi. Kuwana mazita ezvidzidzo zvinodiwa kunogona kuitwa pawebsite ye Maths.
Kutanga KupindaMazita anoshandiswa pano
Tinya chero chiratidzo kuti uone chirevo chakazara, vhidhiyo, uye kuti chii chinoreva chero chiratidzo.
Maitiro: Conic sections
- An expression in x, y. Here is what it does.
Mabvunzo vanhu vanobvunza
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