AP PreCalculus Flashcards: Conic Sections
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
How is a circle defined as a special case of an ellipse in its analytical form?
A circle is a special case of an ellipse where the horizontal radius 'a' is equal to the vertical radius 'b'.
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How is a circle defined as a special case of an ellipse in its analytical form?
A circle is a special case of an ellipse where the horizontal radius 'a' is equal to the vertical radius 'b'.
What is the standard form for an ellipse centered at (h, k)?
The equation is (x-h)²/a² + (y-k)²/b² = 1, where 'a' is the horizontal radius and 'b' is the vertical radius.
Which term's sign in a hyperbola's standard equation determines its orientation (horizontal or vertical)?
The orientation is determined by the positive squared term; if the x-term is positive it opens horizontally, and if the y-term is positive it opens vertically.
Write the analytical representation for a parabola with a horizontal axis of symmetry and vertex at (h, k).
The equation is (x-h) = a(y-k)², where a ≠ 0.
Identify the conic section represented by the equation (x-2)²/16 + (y+1)²/16 = 1.
This represents a circle (a special case of an ellipse) centered at (2, -1) because a=b.
What key feature in the standard equation distinguishes a hyperbola from an ellipse?
A hyperbola's equation has a subtraction sign between the squared terms, while an ellipse's equation has an addition sign.
What is the analytical representation of a parabola with a vertical axis of symmetry and vertex at (h, k)?
The equation is y-k = a(x-h)², where a ≠ 0.
In the standard equations for conic sections, what do the parameters (h, k) represent?
The coordinates (h, k) represent the vertex of a parabola or the center of an ellipse or hyperbola.
What type of conic section is represented by (y-5)²/4 - (x+2)²/9 = 1?
This equation represents a hyperbola centered at (-2, 5) that opens vertically.
What is the standard form for a hyperbola centered at (h, k) that opens horizontally?
The equation is (x-h)²/a² - (y-k)²/b² = 1.