Convert the polar equation to rectangular form.

$$r^2=4\cos2\theta$$

Suspension Bridge Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are $1280$ meters apart. The top of each tower is $152$ meters above the roadway. The cables touch the roadway midway between the towers.

Write an equation that models the cables.

Suspension Bridge Each cable of the Golden Gate Bridge is suspended (in the shape of a parabola) between two towers that are $1280$ meters apart. The top of each tower is $152$ meters above the roadway. The cables touch the roadway midway between the towers.

Draw a sketch of the bridge. Locate the origin of a rectangular coordinate system at the center of the roadway. Label the coordinates of the known points.

Convert the polar equation to rectangular form.

$$r^2=\sin\theta$$

Find $dy/dx$ and $d^2y/dx^2$, and find the slope and concavity (if possible) at the given value of the parameter.

$$\underline{Parametric\ Equation}$$

$$x=t+1,\ y=t^2+3t$$

$$\underline{Point}$$

$$t=-1$$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

$$100x^2+100y^2-100x+400y+409=0$$

Determine whether the statement is true or false. Justify your answer.

The graph of $x^2+4y^4-4=0$ is an ellipse.

Convert the polar equation to rectangular form.

$$r=4\sin\theta$$

Let $(x_1,y_1)$ be the coordinates of a point on the parabola $x^2=4py$. The equation of the line tangent to the parabola at the point is $y-y_1=\frac{x_1}{2p}(x-x_1)$. What is the slope of the tangent line?

Find $dy/dx$ and $d^2y/dx^2$, and find the slope and concavity (if possible) at the given value of the parameter.

$$\underline{Parametric\ Equation}$$

$$x=\sqrt t,\ y=3t-1$$

$$\underline{Point}$$

$$t=1$$

Convert the rectangular equation to polar form. Assume $a>0$.

$$y^2=x^3$$

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

$$9x^2+4y^2-90x+8y+228=0$$

Convert the polar equation to rectangular form.

$$r=8\sin\theta$$

Area Find the dimensions of the rectangle (with sides parallel to the coordinate axes) of maximum area that can be inscribed in the ellipse $x^2/25+y^2/16=1$.