We have been given that an ellipse has a center at the origin, a vertex along the minor axis at (0,-8), and a focus at (15,0). We are asked to find the equation for the ellipse.
The standard from an ellipse centered at origin with major axes at x-axis is [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex], where
a = Horizontal radius,
b = Vertical radius.
Since focus is at x-axis, so our ellipse will be a major horizontal axis.
Horizontal radius will be equal to distance from origin to point (15,0) that is [tex]a=15-0=15[/tex]
The vertical radius would be distance from origin to point (0,-8) that is:
[tex]b=\sqrt{(0-(-8)^2)}=8[/tex]
Upon substituting values of a and b in above equation, we will get:
[tex]\frac{x^2}{15^2}+\frac{y^2}{8^2}=1[/tex]
Therefore, our required equation would be [tex]\frac{x^2}{15^2}+\frac{y^2}{8^2}=1[/tex].
