Chapter 4 Conics Flashcards
What are the possible cross-sections when cutting a double cone with one plane?
The cross-section can be a circle, ellipse, parabola, or hyperbola.
What is the standard form of a circle?
The standard form of a circle is x² + y² = a.
What is the standard form of an ellipse?
The standard form of an ellipse is (x²/a²) + (y²/b²) = 1.
What is the standard form of a parabola?
The standard form of a parabola is y² = 4ac.
What is the standard form of a hyperbola?
The standard form of a hyperbola is (x²/a²) - (y²/b²) = 1.
What are the asymptotes for the hyperbola (x²/a²) - (y²/b²) = 1?
The asymptotes are y = ±(b/a)x.
What does y = f(x) + a represent?
It represents a translation of the curve by a in the y-direction.
What does y = f(x - a) represent?
It represents a translation of the curve by -a in the x-direction.
What does y = af(x) represent?
It represents a stretch of the curve by a scale factor a in the y-direction.
What does y = f(ax) represent?
It represents a stretch of the curve by a scale factor 1/a in the x-direction.
What does y = -f(x) represent?
It is a reflection of the curve in the x-axis.
What does y = f(-x) represent?
It is a reflection of the curve in the y-axis.
What does x = f(y) represent?
It is a reflection of the curve in the line y = x.
What does x = -f(y) represent?
It is a reflection of the curve in the line y = -x.
