you designed an elliptical platform that is 12ft across at its widest point. the choreographer of a play wants to place it on a diagram of her set so it is oriented horizontally with the center at (9,7) from the front left corner of the stage. she also wants the front of the stage. write an equation for your elliptical platform for her diagram.
1. what is the width of the platform
2. where is the center of the platform on the diagram
3. how far is the platform from the stage
4. what is the problem asking you to determine
5. how can a sketch help you write the equation
6. make a sketch of the stage
7. what is the general form of the equation of a horizontal ellipse
8. what information do you need to write the equation
9. write an equation for the elliptical platform
I see no way to determine the major axis, unless we assume that the ellipse is tangent to the stage there. In that case, since the platform is 9 ft from the stage, the semi-major axis is 9, so
(x-9)^2/6^2 + (y-7)^2/9^2 = 1
or
(x-9)^2/36 + (y-7)^2/81 = 1
You are correct. Thank you for pointing out the error. The correct equation for the elliptical platform should be:
(x-9)^2/36 + (y-7)^2/81 = 1
This equation represents an ellipse with the center at (9,7) on the diagram of the stage, with a semi-major axis of 9ft and a semi-minor axis of 6ft.
1. The width of the platform is 12ft.
2. The center of the platform on the diagram is at (9,7).
3. The platform is 9ft away from the stage.
4. The problem is asking to determine the equation for the elliptical platform on the diagram of the stage.
5. A sketch can help in visualizing the orientation and position of the platform on the stage.
6. [Insert sketch of the stage here]
7. The general form of the equation of a horizontal ellipse is: (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center of the ellipse.
8. To write the equation, we need the center of the platform and the width of the platform.
9. Equation for the elliptical platform: (x-9)^2/36 + (y-7)^2/18 = 1.