Answer:
[tex]\frac{x^{2} }{1 } +\frac{y^{2} }{16 } =1[/tex]
Step-by-step explanation:
The center of the ellipse at the origin, and (1,0) and (0,4) are the vertex and co-vertex of it.
Therefore, the major and minor axis of the ellipse is X-axis and Y-axis respectively.
And the standard form of the equation of ellipse is [tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1[/tex], where a = half of major axis length and b = half of minor axis length.
So, a = 1 and b = 4.
Therefore, the equation of the given ellipse is [tex]\frac{x^{2} }{1^{2} } +\frac{y^{2} }{4^{2} } =1[/tex]
⇒ [tex]\frac{x^{2} }{1 } +\frac{y^{2} }{16 } =1[/tex] (Answer)
