Exam 7: Analytic Geometry

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $x ^ { 2 } = 4 p y$ with p > 0, the parabola opens (upward/downward/ left/right).

Choose the one alternative that best completes the statement or answers the question. From the equation of the ellipse, determine if the major axis is horizontal or vertical. - $\frac { x ^ { 2 } } { 11 } + \frac { y ^ { 2 } } { 8 } = 1$

Determine the eccentricity of the ellipse. - $\frac { \left( x - \frac { 1 } { 7 } \right) ^ { 2 } } { 25 } + \frac { \left( y - \frac { 4 } { 3 } \right) ^ { 2 } } { 9 } = 1$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the directrix is horizontal, then the parabola opens (horizontally/vertically).

Write the standard form of the equation of the hyperbola subject to the given conditions. -Vertices: $( - 10 , - 5 ) , ( 2 , - 5 )$ Slope of the asymptotes: $\pm \frac { 1 } { 2 }$

Solve the problem. -The reflective property of an ellipse is the principle behind "whispering galleries". These are rooms with elliptically shaped ceilings such that a person standing at one focus can hear even the slightest whisper spoken By another person standing at the other focus. Suppose that a dome has a semielliptical ceiling, 94 ft long and 22 ft high. Approximately how far from The center along the major axis should each person be standing to hear the "whispering" effect? Round to one decimal place.

Solve the problem. -If a cross-section of the parabolic mirror in a flashlight has the equation $y ^ { 2 } = 7 x$ x, where should the bulb be placed?

Graph the hyperbola. Identify the foci and write the equations for the asymptotes. - $\frac { ( x + 5 ) ^ { 2 } } { 64 } - \frac { ( y + 1 ) ^ { 2 } } { 36 } = 1$

Write the equation of the ellipse in standard form. Identify the center and vertices. - $4 x ^ { 2 } + 16 y ^ { 2 } - 40 x + 96 y + 180 = 0$

An equation of the form $y ^ { 2 } = 4 p x$ is given. Write equations for the directrix and axis of symmetry. - $y ^ { 2 } = - 7 x$

The standard form of an equation of an ellipse centered at the origin with a horizontal major axis is ________, where $a > b > 0$ > 0. If the major axis is vertical, then the equation is ________.

Choose the one alternative that best completes the statement or answers the question. Determine whether the transverse axis and foci of the hyperbola are on the x-axis or the y-axis. - $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 100 } = 1$

Determine the standard form of an equation of the parabola subject to the given conditions. -Vertex: $( - 3 , - 1 )$ ; passes through $( 9,11 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a parabola defined by $y ^ { 2 } = 4 p x$ , the directrix is given by $x = - p$ and the focus is given by the ordered pair .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The________ of a parabola is the point of intersection of the parabola and the axis of symmetry.

Write the standard form of an equation of the ellipse subject to the given conditions. -Vertices: $( 6,1 )$ and $( - 12,1 )$ Foci: $( - 3 - \sqrt { 65 } , 1 )$ and $( - 3 + \sqrt { 65 } , 1 )$

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the vertex and the focus. - $16 y ^ { 2 } - 104 y + 288 x + 1,033 = 0$

Solve the problem. -A parabolic arch forms a structure that allows equal vertical loading along its length. Take the origin at the vertex of the parabolic arch, and write an equation of the parabola.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The line segment perpendicular to the axis of symmetry, passing through the focus and with endpoints on the parabola is called the________ ________ .

Graph the parabola. Find the focus and the endpoints of the latus rectum. - $( y - 1 ) ^ { 2 } = - 12 ( x - 1 )$