91Ó°ÊÓ

Fill in the blanks. Each hyperbola has two ________ that intersect at the center of the hyperbola.

Fill in the blanks. 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.

Fill in the blanks. The polar coordinates \((r, \theta)\) are related to the rectangular coordinates \((x, y)\) as follows: \(x=\) ____ \(y=\) ____ \(\tan \theta=\) _____ \(r^{2}=\) ____

Fill in the blanks. A curve traced out by a point on the circumference of a circle as the circle rolls along a straight line in a plane is called a _______.

Fill in the blanks. The equation \(r=2 \cos \theta\) represents a __________.

Match the conic with its eccentricity. (a) \(01\) (i) parabola (ii) hyperbola (iii) ellipse

The distance between the point \(\left(x_{1}, y_{1}\right)\) and the line \(A x+B y+C=0\) is given by \(d=\)_____.

Fill in the blanks. The line that passes through the focus and the vertex of a parabola is called the _______ of the parabola.

The \(x^{\prime} y^{\prime}\) -coordinate system has been rotated \(\theta\) degrees from the \(x y\) -coordinate system. The coordinates of a point in the \(x y\) -coordinate system are given. Find the coordinates of the point in the rotated coordinate system. $$\theta=90^{\circ},(0,3)$$

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?