Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. x² + 6x - 4y + 1 = 0

Graph each ellipse and give the location of its foci. (x − 1)²/2 + (y +3)² /5= 1

In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes. $4x^2-9y^2-16x+54y-101=0$

In Exercises 43–50, convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes. $4x^2-25y^2-32x+164=0$

Identify each equation without completing the square. y² - 4x + 2y + 21 = 0

Graph each ellipse and give the location of its foci. 9(x − 1)²+4(y+3)² = 36

Identify each equation without completing the square.

$y^2-4x-4y=0$

In Exercises 51–56, graph each relation. Use the relation's graph to determine its domain and range. $\frac{x^2}{9}-\frac{y^2}{16}=1$

Convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci. 9x² +25y² - 36x + 50y – 164 = 0

Identify each equation without completing the square. 4x² - 9y² - 8x - 36y - 68 = 0

Identify each equation without completing the square.

$9x^2+25y^2-54x-200y+256=0$

In Exercises 51–56, graph each relation. Use the relation's graph to determine its domain and range. $\frac{x^2}{9}+\frac{y^2}{16}=1$

Convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci. 9x² + 16y² – 18x + 64y – 71 = 0

Identify each equation without completing the square.

$9x^2+4y^2-36x+8y+31=0$

Convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci. 4x² + y²+ 16x - 6y - 39 = 0

In Exercises 51–56, graph each relation. Use the relation's graph to determine its domain and range. $\frac{y^2}{16}-\frac{x^2}{9}=1$

Identify each equation without completing the square. 100x² - 7y² + 90y - 368 = 0

Identify each equation without completing the square.

$y^2+8x+6y+25=0$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? y² + 6y - x + 5 = 0

Convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci. 25x²+4y² – 150x + 32y + 189 = 0

Convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci. 36x² +9y² - 216x = 0

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function?

$y=-x^2+4x-3$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\begin{cases} x^2 + y^2 = 1 \\ x^2 + 9y^2 = 9 \end{cases}$

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function?

$x=-4(y-1{)}^2+3$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\begin{cases} \frac{x^2}{25} + \frac{y^2}{9} = 1 \\ y = 3 \end{cases}$

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\{\begin{array}{c}{(y-2)}^2=x+4\\ y=-\text{(}\frac{1}{2}\text{)}x\end{array}$

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\{\begin{array}{c}x=y^2-3\\ x=y^2-3y\end{array}$

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations.

$\begin{cases} 4x^2 + y^2 = 4 \\ 2x - y = 2 \end{cases}$

Graph each semiellipse. y = -√16 - 4x²

Find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. $\begin{cases} x = (y + 2)^2 - 1 \\ (x - 2)^2 + (y + 2)^2 = 1 \end{cases}$