Question

Write the equation of the ellipse graphed below.

Answer 1

Answer:

Step-by-step explanation:

This is a horizontally stretched ellipse.  That means that the horizontal line which is represented by the x-axis is the longer one.  The equation for this type of ellipse is

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

In an ellipse, the a value is ALWAYS bigger than the b value, and since the x-axis represents the longer axis, the a goes under the x-squared term.  

To solve for the h, the k, the a, and the b, we simply have to do some counting.  The center of the ellipse, the (h, k) our of equation, is sitting at (4, 6).  Put them where they belong in the equation.  The a axis (the horizontal one) is 8 units long, and the b axis (the vertical one) is 4 units long.  Square both of them and put them where they belong in the equation:

$\frac{(x-4)^2}{64}+\frac{(y-6)^2}{16} =1$

There you go!