Conics Flashcards
(11 cards)
What are the possible cross-sections when cutting a double cone with one plane?
The cross-section can be a circle, an ellipse, a parabola, or a hyperbola.
What is the standard form of a parabola?
The standard form of a parabola is y = 4ax.
What are the transformations that can be applied to a curve defined by g(x, y) = 0?
Transformations include translation, reflection, stretching, rotation, and enlargement.
What does reflection in the y-axis do to the function g(x, y)?
It transforms to g(-x, y) = 0.
What is the result of translating the function g(x, y) by a units in the positive y-direction?
The result is g(x, y - a) = 0.
What is the effect of rotating a function by 180° about the origin?
The function transforms to g(-x, -y) = 0.
What is the significance of the order of transformations?
The order of transformations matters; changing it can result in a different curve.
How can completing the square assist in transformations?
Completing the square can help to find the transformation that has been applied.
What is the standard form of am ellipse?
What is the standard form of a hyperbola?
What is the standard form of a circle?
