Question

A room is built in the shape of an ellipse with length 14 feet and width 4 feet. using a horizontal ellipse, what is the standard form of the equation of the ellipse representing the outline of room if the center of the room is represented by the point (0,0)?

A. X²/49 + Y2/4 = 1
B. X²/196 + Y2/16 = 1
C. X²/4 + Y2/49 = 1
D. X²/16 + Y2/196 = 1

Answer 1

The standard form of the equation of the ellipse representing the outline of the room is x^2/196 + y^2/16 = 1.

Step-by-step explanation:

To find the standard form of the equation for the ellipse representing the outline of the room, we need to use the formula for the equation of an ellipse:

(x - h)2/a2 + (y - k)2/b2 = 1

where (h,k) is the center of the ellipse and a and b are the lengths of the major and minor axes respectively. In this case, the center of the room is represented by the point (0,0), the length of the ellipse is 14 feet, and the width of the ellipse is 4 feet.

Plugging these values into the standard form equation, we get:

(x - 0)2/142 + (y - 0)2/42 = 1

Simplifying, we get:

x2/196 + y2/16 = 1

Therefore, the standard form of the equation of the ellipse representing the outline of the room is option B: x2/196 + y2/16 = 1.