Exam 14: Foundations: a Prelude to Functions

Solve the problem. -Find an equation of the line containing the centers of the two circles $x ^ { 2 } + y ^ { 2 } + 2 x - 12 y + 36 = 0 \quad$ and $x ^ { 2 } + y ^ { 2 } + 12 x + 2 y + 33 = 0$

Find the distance d(P1, P2) between the points P1 and P2. -

Find the midpoint of the line segment joining the points P1 and P2. - $\mathrm { P } _ { 1 } = ( 6,5 ) ; \mathrm { P } _ { 2 } = ( 8,1 )$

Plot the point. - $( 3,6 )$

List the intercepts for the graph of the equation. -y2 = x + 49

Graph the equation by plotting points. - $x^{2}+4 y=4$

Find an equation for the line with the given properties. -Parallel to the line x - 5y = 5; containing the point (0, 0)

Find the center (h, k) and radius r of the circle with the given equation. - $x ^ { 2 } + y ^ { 2 } - 4 x + 8 y = 29$

Find the slope and y-intercept of the line. - $9 x - 11 y = 99$

Find the slope of the line. -

Find the center (h, k) and radius r of the circle with the given equation. - $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 9$

Find the distance d(P1, P2) between the points P1 and P2. -

Solve the problem. -Find the area of the right triangle $\mathrm { ABC }$ with $\mathrm { A } = ( - 2,7 ) , \mathrm { B } = ( 7 , - 1 ) , \mathrm { C } = ( 3,9 )$ .

Draw a complete graph so that it has the given type of symmetry. - $\text { origin }$

Find an equation for the line with the given properties. -Vertical line; containing the point $( 8.8,5.7 )$

Plot the point. - $(1,-4)$

Find the general form of the equation of the the circle. -Center at the point $( - 4 , - 3 )$ ; containing the point $( - 3,3 )$

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. -

Decide whether the pair of lines is parallel, perpendicular, or neither. - 3x-4y=-2 8x+6y=16

Graph the equation by plotting points. - $y=-x^{2}+4$