Question

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Answer 1

Answer:

10 units

Step-by-step explanation:

General equation of an ellipse

$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1 \quad \textsf{where }(h \pm a,k)\: \textsf{and}\:(h, k \pm b)\: \textsf{are the vertices}$

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:

$\dfrac{(y-4)^2}{25}+\dfrac{x^2}{9}=1$

$\implies \dfrac{x^2}{9}+\dfrac{(y-4)^2}{25}=1$

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)