8. Conic Sections

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\(\end{cases}\)$

Graph each ellipse and give the location of its foci. (x +3)²/9 + (y -2)² = 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. 25x²+4y² – 150x + 32y + 189 = 0

The equation of the red ellipse in the figure shown is x^2/25 + y^2/9 =1Write the equation for each circle shown in the figure.

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

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

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (-4,0), (4,0); Vertices: (-5,0) (5,0)

Graph each ellipse and locate the foci. x²/9 +y²/36= 1

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0); y-intercepts: -3 and 3

Determine the vertices and foci of the following ellipse: $\(\frac{x^2}{49}\)+\(\frac{y^2}{36}\)=1$.

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-5, 0), (5, 0); vertices: (-8, 0), (8,0)

Graph the ellipse and locate the foci. $\frac{x^2}{36}+\frac{y^2}{25}=1$

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

Graph the ellipse $\frac{{(x-1)}^2}{9}+\frac{{(y+3)}^2}{4}=1$.