Identify the type of curve for each equation, and then view it on a calculator.

$$4(y^2 + 6y + 1) = x(x - 4) - 24$$

Plot the given curves in polar coordinates.

$$r=\frac{3}{\sin \theta+2\cos \theta}$$

Determine the center and radius of each circle. Sketch each circle

$$2x^2 + 2y^2 = 4x + 8y + 1$$

Find the polar equation of each of the given rectangular equations.

$$x^2 +4y^2=4$$

Determine the center (or vertex if the curve is a parabola) of the given curve. Sketch each curve.

$$16x^2 + 25y^2 - 32x + 100y - 284 = 0$$

View the curves of the given polar equations on a calculator.

$$r= 2 \sec \theta + 1$$

Solve the given problems.

The equation of an ellipse with center $(h,k)$ and major axis parallel to the $x$-axis is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$. Sketch the ellipse that has a major axis of $6$, a minor axis of $4$, and for which is $(h,k)$ is $(2,-1)$

Determine the center and radius of each circle. Sketch each circle

$$9x^2 + 9y^2+18y=7$$

Solve the given problems.

Find the equation of the parabola with focus $(6,1)$ and directrix $x=0$, by use of the definition. Sketch the curve.

Determine whether the given lines are parallel, perpendicular, or neither

$48y - 36x = 71$ and $52x = 17 - 39y$

Solve the given problems.

Use a calculator to view the ellipse $4x^2 + 8y^2 + 4x - 24y + 1 = 0$

View the curves of the given polar equations on a calculator.

$$r=0.5^{\sin \theta}$$

Determine whether the lines through the two pairs of points are parallel or perpendicular.

$(-3,9)$ and $(4,4)$;$(9,-1)$ and $(4,-8)$

Identify the type of curve for each equation, and then view it on a calculator.

$$2(2x^2 - y) = 8 - y^2$$