Question

Write the equation of the ellipse with its center at the origin. the height of the ellipse is 12 units and the width is 14 units.

Answer 1

Sketch the ellipse as shown in the figure below.

The general form of the equation of an ellipse centered at (h,k), with semi -major axis of a and semi - minor axis of b is

`((x-h)^(2))/(a^(2))+ ((y-k)^(2))/(b^(2)) =1`

Because the width is 14, therefore a = 7.
Because the height is 12, therefore b = 6.
Because the ellipse is centered at the origin, h=0, and k=0.

Answer:

`(x^(2))/(49) + (y^(2))/(36) =1`