questions over assignment 3r- one more thing we need to do on 8, 9, & 10
TRANSCRIPT
Ellipse: Given two points F and F' (called the foci), the ellipse is the set of points whose sum of distances to the foci is constant.
Vocabulary
Vocabulary
Center: A point inside the ellipse which is the midpoint of the line segment linking the two foci. The intersection of the major and minor axes.
Vocabulary
Focus Points/Foci: The points from which the ellipse is defined. “The ellipse is the set of points whose sum of distances to the foci is constant.”
P is a point on the Ellipse
Vocabulary
Vertex: Where the Major Axis intersects with the ellipse
Co-Vertex: Where the Minor axis intersects with the ellipse
Equations of Ellipses (Horizontal, Centered at the Origin)
Foci: (-c,0) and (c,0)Vertices: (-a,0) and (a,0)Co-vertices: (0,-b) and (0,b)
Equations of Ellipses (Vertical, Centered at the Origin)
Foci: (0, -c) and (0, c)Vertices: (0, -a) and (0, a)Co-vertices: (-b,0) and (-b,0)
Equ
atio
n fo
r th
e F
oci
Yes, this comes from Pythagorean Theorem. No, the variables used are not the same.No, C is not the hypotenuse.Yes, that can be confusing.No, you do not need to remember where this formula comes from.Yes, you should be able to use it, though.
Example Problem:>Sketch the graph and find the vertices, co-vertices, and foci points for: x² + 4y² = 16
Solution: First put the equation in the correct form by dividing everything by 16: x²/16 + y²/4 = 1 Since the larger value is under x, the ellipse has a horizontal major axis, so a² = 16 and b² = 4. >The values are a = 4, b = 2.>To find c, use c2=a2-b2, c2=16 – 4 c= 3.5
Center at (0, 0) Vertices: (4, 0) and (-4, 0) Co-Vertices: (0, 2) and (0, -2) Foci: (3.5, 0) and (-3.5, 0)
Center at (0, 0) Vertices: (4, 0) and (-4, 0) End Co-Vertices: (0, 2) and (0, -2) Foci: (3.5, 0) and (-3.5, 0)