ALGEBRA II HONORS/GIFTED - ELLIPSES

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Presentation transcript:

ALGEBRA II HONORS/GIFTED - ELLIPSES 12/9/2018 ALGEBRA II HONORS/GIFTED @ ELLIPSES

Desmos.com (again). https://www.desmos.com/calculator/ccxb11vkxw

ALGEBRA II HONORS/GIFTED - ELLIPSES 12/9/2018 ELLIPSES Standard Form ax2 + by2 + cx + dy + e = 0 Center Radius Form MUST be 1 for a ellipse!!! (h, k) center rx= x-radius ry= y-radius

Major Axis: long axis all the way across the ellipse Minor Axis: short axis all the way across the ellipse Semi-major axis: half of the major axis Semi-Minor Axis: half the minor axis X-radius: the distance from the center to the ellipse in the x-direction Y-radius: the distance from the center to the ellipse in the y-direction Minor Axis Vertex

What is a Focal Radius? If a is the length of the semi-major axis It is the distance from the center to the focus. If a is the length of the semi-major axis b is the length of the semi-minor axis, and c is the focal radius, and d1 and d2 are the distances from a point (x , y) on an ellipse to the two foci. Then d1 + d2 = 2a = the length of the major axis, a2 = b2 + c2, from which c2 = a2 - b2 The formula to find the focal radius! (x,y) d1 d2 b a c

1) Standard Form to Center Radius Form ALGEBRA II HONORS/GIFTED - ELLIPSES 1) Standard Form to Center Radius Form 12/9/2018 25x2 + 9y2 - 200x + 18y + 184 = 0 IMPORTANT INFORMATION Center rx ry rf Length of major axis Length of minor axis

ALGEBRA II HONORS/GIFTED - ELLIPSES 2) Standard Form to Center Radius Form 12/9/2018 25x2 + 49y2 – 100x + 392y – 341 = 0 IMPORTANT INFORMATION Center rx ry rf Length of major axis Length of minor axis

3) Find the equation of the ellipse with center (2, 5), one focus (5, 5) and one vertex (7, 5).

ELLIPSES IN EVERYDAY LIFE