Answer
$\dfrac{(x-1)^2}{100}+\dfrac{(y+4)^2}{64}=1$
Work Step by Step
The standard form of the equation of the ellipse when the major axis is horizontal can be expressed as: $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$ in which $(h,k)$ is the center, $2a$ is the major axis length, and $2b$ is the minor axis length.
The standard form of the equation of the ellipse when the major axis is vertical can be expressed as: $\dfrac{(x-h)^2}{b^2}+\dfrac{(y-k)^2}{a^2}=1$ in which $(h,k)$ is the center, $2a$ is the major axis length, and $2b$ is the minor axis length.
The ellipse is in the horizontal axis, so the distance between the vertices is equal to $2a$:
$b=\sqrt{a^2-c^2}=\sqrt {(10)^2-6^2}=\sqrt {64}=8$
$\dfrac{(x-1)^2}{10^2}+\dfrac{(y+4)^2}{8^2}=1$
or, $\dfrac{(x-1)^2}{100}+\dfrac{(y+4)^2}{64}=1$
