8. Conic Sections

Graph each ellipse and give the location of its foci. (x +3)²+ 4(y -2)² = 16

Graph each ellipse and give the location of its foci. (x − 4)²/9 + (y +2)² /25= 1

Graph each ellipse and give the location of its foci. x²/25 + (y -2)² /36= 1

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

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

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. 4x² - 9y² - 8x - 36y - 68 = 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. 9x² +25y² - 36x + 50y – 164 = 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. 9x² + 16y² – 18x + 64y – 71 = 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. 4x² + y²+ 16x - 6y - 39 = 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

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.

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

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.

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