Graph and Write Equations of Ellipses Notes 9.4 (Day 1) Graph and Write Equations of Ellipses

Vocab!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Ellipse: Like an oval Foci: Plural for focus Sum of the distances from the foci to any point on the ellipse remains constant

More Vocab  Major Axis: The axis that goes through the foci and center point Minor Axis: The axis that only goes through the center point

Even More VOCABULARY!! Vertices: The points that are farthest from the origin on the major axis Co-Vertices: The points that are the farthest from the origin on the minor axis

Graphing Ellipses Ellipses: h and k are both the opposite of what you think (just like a circle) (h, k) is the center point of the ellipse.

Standard Equation of an Ellipse Major axis: Horizontal Vertices: Co-Vertices: IMPORTANT!!! ***The a value is always the greater number. Focus Points: OR

Standard Equation of an Ellipse Major axis: Vertices: Co-Vertices: Vertical IMPORTANT!!! ***The a value is always the greater number. Focus Points: OR

How to graph an ellipse: Step 1: Determine whether a (the bigger number) is underneath x2 or y2. Step 2: Find both the a and b values by square rooting the numbers under x2 and y2. Step 3: Draw a coordinate plane. Step 4: Place your center point at (h, k), this is your new “origin” Step 4: Label the vertices (a) and co-vertices (b) (Depends on whether a is under x2 or y2) Step 5: Find the foci. (c2 = a2 – b2, *don’t forget to square root*) Step 6: Graph the foci.

Graph the equation. List the vertices, co-vertices, major axis, and focus points.

Graph the equation. List the vertices, co-vertices, major axis, and focus points.

Graph the equation. List the vertices, co-vertices, major axis, and focus points.

Graph the equation. List the vertices, co-vertices, major axis, and focus points.

Putting the Ellipse into Standard Form: Step 1: Solve for the constant Step 2: Complete the square with both the x and y values Step 3: Divide both sides by the appropriate number to make the constant equal to 1

Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

Put the ellipse into standard form to identify the center point, the foci, the vertices, and the co-vertices.

Homework: Graphing and Properties of Ellipses