Conics Flashcards
What is the equation of an ellipse in standard position?
x^2/a^2 + y^2/b^2 = 1
State an expression for the term “b^2” in the equation of an ellipse in standard position.
b^2=a^2(1-e)
At what points does an ellipse in standard position intersect the coordinate axes?
(+|- a, 0) and (0, +|-b)
What is the equation for the eccentricity e of an ellipse in standard position?
e = sqrt(1 - b^2/a^2)
How can an ellipse in standard position be obtained from the circle with equation x^2 + y^2 = a^2?
By a vertical scaling of factor b/a.
State the focus-directrix definition of a parabola.
PF = Pd
State the focus-directrix definition of an ellipse.
PF = ePd where 0
State the focus-directrix definition of an hyperbola.
PF = ePd, where e>1
What is the equation of an hyperbola in standard position?
x^2/a^2 - y^2/b^2 = 1
Give an equation for the term “b^2” in the equation of an hyperbola in standard position.
b^2 = a^2(e^2-1), where b>0.
Give an equation for the eccentricity e if an hyperbola in standard position.
e = sqrt(1 + b^2/a^2)
What is the vertex of a standard parabola?
The origin, (0,0)
What is the focus of a standard parabola?
(a,0)
What is the directrix of a standard parabola?
x = -a
A parabola in standard position always passes through which two points? (State the points in terms of a).
(a, +|- 2a)
