Respuesta :
Answer:
[tex]\frac{x^{2} }{36}+\frac{y^2}{16}=1[/tex]
Step-by-step explanation:
Center of the ellipse is at origin (0, 0)
So (h, k) = (0, 0)
Length of major axis = 12
2a = 12
⇒ a = 6
Length of minor axis = 8
⇒ 2b = 8
⇒ b = 4
Since focus is on the x-axis, so it's a horizontal ellipse.
Equation of the horizontal ellipse is in the form of,
[tex]\frac{(x-h)^{2} }{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
By substituting the given values of a, b, and (h, k)
[tex]\frac{(x-0)^{2}}{6^2}+\frac{(y-0)^2}{4^2}=1[/tex]
[tex]\frac{x^{2} }{36}+\frac{y^2}{16}=1[/tex]
