Precalculus, Unit 8: Conics and Polar Coordinates. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
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- What is a conic section?
- A curve formed by intersecting a plane with a double cone
- What are the four types of conic sections?
- Circle, ellipse, parabola, and hyperbola
- What is the standard equation of a circle?
- (x-h)^2 + (y-k)^2 = r^2
- What is the standard equation of an ellipse centered at the origin?
- x^2/a^2 + y^2/b^2 = 1
- What is the standard equation of a hyperbola centered at the origin, opening left/right?
- x^2/a^2 - y^2/b^2 = 1
- What is eccentricity?
- A measure of how much a conic section deviates from being circular
- What eccentricity describes a parabola?
- Exactly 1
- What is a polar coordinate system?
- A coordinate system using a distance and an angle from a fixed point, instead of x and y
- What is the pole in a polar coordinate system?
- The fixed reference point, equivalent to the origin
- What is the polar axis?
- The reference ray from which angles are measured, equivalent to the positive x-axis
- How do you convert polar coordinates (r, theta) to rectangular coordinates?
- x = r cos(theta), y = r sin(theta)
- How do you convert rectangular coordinates (x, y) to polar coordinates?
- r = sqrt(x^2+y^2), theta = arctan(y/x)
- What is a polar equation?
- An equation expressed in terms of r and theta instead of x and y
- What shape does the polar equation r = a produce?
- A circle of radius a centered at the pole
- What shape does the polar equation theta = k produce?
- A straight line through the pole
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