91Ó°ÊÓ

Make a table of values for each of the following equations and graph the two equations on the same set of axes. \(y=x+3\) \(y=x-1\)

Find the center, the radius, the diameter, the circumference, and the area of the circle represented by each equation. \(\mathbf{a.} x^{2}+y^{2}=36\) b. \((x+5)^{2}+y^{2}=\frac{9}{4}\) c. \((x-3)^{2}+(y+6)^{2}=100\) \(d. \frac{(x+5)^{2}}{3}+\frac{(y-2)^{2}}{3}=27\)

Determine the intersection of the solution sets of the two inequalities \(y>2\) and \(x+2 y<6\) by graphing.

Find the distance between the points of intersection of the graph of \(x^{2}+y^{2}=17\) and the graph of \(x+y=3\).

The vertices of a right triangle are \((0,0),(3,0),\) and \((3,4)\) a Find the lengths of the three sides. b Find the length of the altitude to the hypotenuse. c Find the length of the median to the hypotenuse.

Consider the circle represented by \((x-2)^{2}+(y+3)^{2}=61\) Write, in point- slope form, the equation of the tangent to the circle at point \((8,-8)\).

A square with vertices at \(\mathrm{A}=(1,1), \mathrm{B}=(0,4), \mathrm{C}=(3,5),\) and \(\mathrm{D}=(4,2)\) is reflected over the \(\mathrm{x}\) -axis to produce a new square with vertices \(A^{\prime}, B^{\prime}, C^{\prime},\) and \(D^{\prime}\) a Find the area of square \(\mathrm{A}^{\prime} \mathrm{B}^{\prime} \mathrm{C}^{\prime} \mathrm{D}^{\prime}\) b Find, in \(y\) -form, the equation of \(\overleftarrow{A^{\prime} C^{\prime}}\)

The point \((13,9)\) is on a circle centered at \((7,1)\) a Write an equation of the circle. b What is the circle's area? c What is the circle's circumference? d Find the coordinates of the point on the circle directly opposite \((13,9)\) e Write, in point-slope form, an equation of the line tangent to the circle at \((13,9)\) f Find the distance between ( \(19,6\) ) and the center of the circle. g Find the distance between \((19,6)\) and the circle.

A parallelogram has vertices \((-5,-1),(4,-1),\) and \((7,6) .\) Find the fourth vertex if two sides are parallel to the \(x\) -axis.

A line passes through a point 3 units to the left of and 2 units above the origin. Write an equation of the line if it is parallel to a The \(x\) -axis b The y-axis