Exam 11: Analytic Geometry

Give the focus, directrix, and axis for the parabola. -A cross-section of an irrigation canal is a parabola. If the surface of the water is 48 ft wide and the canal is 7 ft deep at the center, how deep is it 24 ft from the edge?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $5 x ^ { 2 } - y = 14$

Provide an appropriate response. -Explain why the graph of a hyperbola does not satisfy the conditions for the graph of a function.

Write an equation for the hyperbola. -vertices at $( 5,0 ) , ( - 5,0 )$ ; foci at $( 9,0 ) , ( - 9,0 )$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( y - 2 ) ^ { 2 } } { 144 } - \frac { ( x - 4 ) ^ { 2 } } { 81 } = 1$

Match the equation of the parabola with the appropriate description. - $x = 2 y ^ { 2 } - 6 y + 5$

Find the eccentricity of the conic section shown in the graph. -When a certain satellite was at a maximum distance of $59.5 \times 10 ^ { 6 }$ m from Earth's center, it had a velocity of 4228 m per sec. Determine the shape of its trajectory.

Provide an appropriate response. -The hyperbola with equation $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 36 } = 1 \text { opens up and down. }$

Identify the type of graph. - $( x + 6 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + 11 = 0$

Give the focus, directrix, and axis for the parabola. -A projectile is thrown upward so that its distance above the ground after t seconds is $\mathrm { h } = - 14 \mathrm { t } ^ { 2 } + 476 \mathrm { t }$ After how many seconds does it reach its maximum height?

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $14 y = 4 ( x + 4 ) ^ { 2 }$

Identify the type of graph. - $\frac { ( x - 7 ) ^ { 2 } } { 3 } + \frac { ( y - 3 ) ^ { 2 } } { 7 } = 0$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x + 3 = ( y + 6 ) ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $x = 10 y ^ { 2 }$

Find the eccentricity of the conic section shown in the graph. - $x = - 21$

Graph the ellipse. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$

Provide an appropriate response. -Why is it not possible to choose h and k, neither zero, so the parabola $f ( x ) = a ( x - h ) ^ { 2 } + k$ has its vertex at the origin?

Match the equation of the ellipse with the appropriate description. - $49 y ^ { 2 } = 4900 - 4 x ^ { 2 }$

Graph the conic section. - $25 y^{2}-16 x^{2}=400$