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
$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} =1$

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:
$\frac{x^{2}}{49} + \frac{y^{2}}{36} =1$