Coordinate systems Flashcards
What is a parametric equation?
An equation in which both the x and y values are expressed in the form of independent variable, i.e. x=f(t), y=g(t)
What is a Cartesian equation?
An equation in terms of x and y only
How can a parametric equation be converted into a Cartesian equation?
By rearranging one of the equations to give t in terms of x or y, and then substituting t for this in the other equation
What are the parametric equations of a parabola?
x=at², y=2at where a is a constant
What is the Cartesian equation of the parametric equations x=at², y=2at where a is a constant?
y²=4ax
What is a locus?
A set of points which obey certain rules
What is the definition of a parabola?
The locus of points that are equidistant from both a point (the focus) and a straight line (the directrix)
For a parabola with equation y²=4ax, what are the coordinates of the focus?
(a,0)
For a parabola with equation y²=4ax, what is the equation of the directrix?
x=-a
What are the parametric equations of a hyperbola?
x=ct, y=c/t where c is a constant
What is the Cartesian equation of the parametric equations x=ct, y=c/t where c is a constant?
xy=c²
What is the definition of a hyperbola?
Given two foci, it is the locus of points such that the difference between the distances to each focus is constant
