Question

Write the equation in standard form for the ellipse with center at the origin, vertex (-8, 0), and co-vertex (0,4).​

Answer 1

Answer:     $\dfrac{x^2}{64}+\dfrac{y^2}{16}=1$

Step-by-step explanation:

The standard form for an ellipse is:   $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$    where

• (h, k) is the center
• a is the radius on the x-axis
• b is the radius on the y-axis

Given: (h, k) = (0, 0)

a = 8 (distance on x-axis from origin to -8)

b = 4 (distance on y-axis from origin to 4)

Input h = 0, k = 0, a = 8, b = 4 into the standard form for an ellipse:

                                    $\dfrac{(x-0)^2}{8^2}+\dfrac{(y-0)^2}{4^2}=1$

                                  $=\dfrac{x^2}{64}+\dfrac{y^2}{16}=1$