Answer:
The equation of a vertical ellipse is [tex]\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\[/tex]
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 :
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\\[/tex]
Now, substituting the values, a, b , h and k in above expression, we get:
[tex]\frac{(x-6)^2}{10^2} + \frac{(y-3)^2}{6^2} = 1\\[/tex]
or, [tex]\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\[/tex]
Hence, the equation of a vertical ellipse is [tex]\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\[/tex]
