Question

Write the equation of the ellipse in standard form that has the following characteristics: Vertices (2,1) (2,7) and co-vertices (0,4) (4,4)

Answer 1

Answer:

$\frac{(x - 2)^{2} }{4 } + \frac{(y - 4)^{2} }{9 } = 1$

Step-by-step explanation:

Equation of an ellipse elongated vertically in standard form is$\frac{(x - h)^{2} }{b^{2} } + \frac{(y - k)^{2} }{a^{2} } = 1$:    for where (h, k) is the center, a is the distance

from the center to a vertex, b is the distance from the center to a co-vertex.

In your problem, the center is at (2, 4),  a = 3 and b = 2

So, the equation is  $\frac{(x - 2)^{2} }{2^{2} } + \frac{(y - 4)^{2} }{3^{2} } = 1$

                                $\frac{(x - 2)^{2} }{4 } + \frac{(y - 4)^{2} }{9 } = 1$