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Magazine Problem 4
A ____________ is defined as the set of all points \((x, y)\) in a plane that are equidistant from a fixed line, called the ____________ and a fixed point, called the ____________, not on the line.
Problem 4
The concept of ________ is used to measure the ovalness of an ellipse.
Problem 4
The equation \(r=2 \cos \theta\) represents a ___________.
Problem 4
Each hyperbola has two ___________ that intersect at the center of the hyperbola.
Problem 4
The distance between the point \(\left(x_{1}, y_{1}\right)\) and the line \(A x+B y+C=0\) is given by \(d=\) ______________.
Problem 5
The line that passes through the focus and the vertex of a parabola is called the _____________ of the parabola.
Problem 5
Consider the parametric equations \(x=\sqrt{t}\) and \(y=3-t\) (a) Create a table of \(x\) - and \(y\) -values using \(t=0,1,2\), \(3,\) and 4 . (b) Plot the points \((x, y)\) generated in part (a), and sketch a graph of the parametric equations. (c) Find the rectangular equation by eliminating the parameter. Sketch its graph. How do the graphs differ?
Problem 5
The equation \(r^{2}=4 \sin 2 \theta\) represents a ________________.
Problem 5
Write the polar equation of the conic for \(e=1, e=0.5,\) and \(e=1.5 .\) Identify the conic for each equation. Verify your answers with a graphing utility. \(r=\frac{2 e}{1+e \cos \theta}\)
Problem 5
Plot the point given in polar coordinates and find two additional polar representations of the point, using \(-2 \pi<\theta<2 \pi\). \(\left(2, \frac{5 \pi}{6}\right)\)
