Answer:
10 units
Step-by-step explanation:
General equation of an ellipse
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1 \quad \textsf{where }(h \pm a,k)\: \textsf{and}\:(h, k \pm b)\: \textsf{are the vertices}[/tex]
Major Axis: longest diameter of an ellipse
Minor Axis: shortest diameter of an ellipse
Major radius: one half of the major axis
Minor radius: one half of the minor axis
If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical and b is the major radius, and a is the minor radius.
Given equation:
[tex]\dfrac{(y-4)^2}{25}+\dfrac{x^2}{9}=1[/tex]
[tex]\implies \dfrac{x^2}{9}+\dfrac{(y-4)^2}{25}=1[/tex]
Comparing with the general equation:
- h = 0
- a² = 9 ⇒ a = 3
- k = 4
- b² = 25 ⇒ b = 5
As b > a then the ellipse is vertical and b is the major radius.
⇒ Major axis = 2 × Major Radius
= 2b
= 2 × 5
= 10
Also, the vertices are:
- (3, 4) and (-3 ,4)
- (0, 9) and (0, -1)
