91Ó°ÊÓ

Suspension Bridge - The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?

In Problems 67–74, analyze each conic.

$\frac{{\left(y+2\right)}^2}{16}-\frac{{\left(x-2\right)}^2}{4}=1$

Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river $20$meters wide. The center of the arch is $6$meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

Searchlight - A searchlight is shaped like a paraboloid of

revolution. If the light source is located 2 feet from the base

along the axis of symmetry and the opening is 5 feet across,

how deep should the searchlight be?

In Problems 67–74, analyze each conic.

$x^2=16(y-3)$

Except for degenerate cases, the equation$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$defines an ellipse if ________ .

Identify the conic that each polar equation represents. Also, give the position of the directrix.

$r=\frac{1}{1+\cos \left(\mathrm{θ}\right)}$

Answer the following problem using the figure,

If a > 0 the equation of the parabola is of the form:

$$\begin{gathered} a){\left(y-k\right)}^2=4a\left(x-h\right) \\ b){\left(y-k\right)}^2=-4a\left(x-h\right) \\ c){\left(x-h\right)}^2=4a\left(y-k\right) \\ d){\left(x-h\right)}^2=-4a\left(y-k\right) \end{gathered}$$

graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of curve. Verify your graph using a graphing utility.
$x=3t+2,y=t+1;0≤t≤4$

A(n) ______________ is the collection of points in the plane the difference of whose distances from two fixed points is a constant.