Exam 13: Conic Sections

Find an equation of the circle with the given center and radius. -The area of an ellipse given by the equation $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ is $\pi a b$ . A homeowner is building an elliptical swimming pool that is 20 feet from end to end at its longest point, and 12 feet from side to side at its widest point. Find the area covered by the swimming pool. Round to the nearest tenth of a foot if necessary.

Find an equation of the circle with the given center and radius. -Center (0, 0), radius 19

Solve the system by the substitution method. - 16+4=64 2y-4x=8

Find an equation of the circle with the given center and radius. -Center (1, -3), radius 1

Solve. -The diagonal of a Persian rug measures $26 \mathrm { ft }$ . The area of the rug is $240 \mathrm { ft } ^ { 2 }$ . Find the dimensions of the rug.

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( - 7 , - 3 )$ and $( 1,1 )$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( 3 , - 7 )$ and $( 6 , - 1 )$

Graph the ellipse. Give the coordinates of the center, as well as the values of a and b. - $x = - y ^ { 2 } - 4 y - 5$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( 7,1 )$ and $( - 2 , - 1 )$

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( 5 , - 4 )$ and $( 1 , - 1 )$

Solve. - $x ^ { 2 } + y ^ { 2 } - 10 x - 8 y + 16 = 0$

Find an equation of the circle with the given center and radius. -The area of an ellipse given by the equation $\frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1$ is $\pi a b$ . A small park in the shape of an ellipse covers an area of $1884.96$ square meters. The park measures 60 meters from east to west, what is the distance from north to south?

Solve. -Find the dimensions of a rectangular enclosure with perimeter $46 \mathrm { yd }$ and area $126 \mathrm { yd } ^{2}$ .

Solve the problem. -Arches in the shapes of parabolas are often used in construction. Find the equation of a parabolic arc that is 18 feet high at its highest point and 26 feet wide at the base, as illustrated in the figure. Place the origin at the midpoint of the base.

Solve the problem. -An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 4 inches tall and stand 40 inches apart. At some point along the road from the Lowest point of the cable, the cable is 0.36 inches above the roadway. Find the distance between That point and the base of the nearest tower.

Solve the problem. -A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 154 feet and a maximum height of 30 feet. Find the height of the arch at 20 feet from its center.

Find the midpoint of the line segment that connects the given points. - $( 0 , - 2 )$ and $( 9,6 )$

Find the midpoint of the line segment that connects the given points. - $( - 5 , - 6 )$ and $( 5 , - 3 )$

Solve the system by the substitution method. - y=10x- 2x-y=-15

Find the distance between the pair of points. Round to the nearest tenth if necessary. - $( 3,7 )$ and $( - 5 , - 7 )$