# How do you write an equation of an ellipse given the endpoints of major axis at (10,2) and (-8,2), foci at (6,2) and (-4,2)?

Oct 28, 2016

The equation is $\frac{{\left(x - 1\right)}^{2}}{81} + \frac{{\left(y - 2\right)}^{2}}{56} = 1$

#### Explanation:

We have here a horitontal major axis:
The center is $\left(\frac{10 - 8}{2} , 2\right) = \left(1 , 2\right)$
the major axis is $a = 10 - 1 = 9$
The distance focus to center is $5$
So we can calculate b from ${b}^{2} = {a}^{2} - {c}^{2}$
${b}^{2} = 81 - 25 = 56$

The equation of the ellipseis ${\left(x - h\right)}^{2} / {a}^{2} + {\left(y - k\right)}^{2} / {b}^{2} = 1$

here $\left(h , k\right) = \left(\right) 1 , 2$ and $a = 9$ And $b = \sqrt{56}$

So the equation is $\frac{{\left(x - 1\right)}^{2}}{81} + \frac{{\left(y - 2\right)}^{2}}{56} = 1$