Question

An ellipse has a vertex at (1,0), a co-vertex at (0,4), and a center at the origin. Which is the equation of the ellipse in standard form?
x^2/16+y^2/1=1

x^2/1+y^2/4=1

x^2/4+y^2/1=1

x^2/1+y^2/16=1

Answer 1

Answer:

$\frac{x^{2} }{1 } +\frac{y^{2} }{16 } =1$

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 $\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1$, 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 $\frac{x^{2} }{1^{2} } +\frac{y^{2} }{4^{2} } =1$

⇒  $\frac{x^{2} }{1 } +\frac{y^{2} }{16 } =1$ (Answer)