Question

Write the equation of a vertical ellipse with a major axis of 20, a minor axis of 12, and a center of (6, 3)

Answer 1

Answer:

The equation of a vertical ellipse is  $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1$

Step-by-step explanation:

Here, given:

Length of major axis:  20

⇒ 2 a  = 20  , or , a = 10

Length of minor axis:  12

⇒ 2 b  = 12  , or , b = 6

Also, center (h,k)  = (6,3)

Now, STANDARD EQUATION OF ELLIPSE :

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$

Now, substituting the values, a, b , h and k in above expression, we get:

$\frac{(x-6)^2}{10^2} + \frac{(y-3)^2}{6^2} = 1$

or, $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1$

Hence, the equation of a vertical ellipse is  $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1$