Question

For the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$, the value of a is _____ , the value of b is _____ , and the major axis is the ____ -axis.

Short answer

For the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$, the value of a is $\mathbf{5}$, the value of b is $\mathbf{3}$ , and the major axis is the $\mathit{x}\mathbf{-}$axis.

Step-by-step solution

Step 1. Given Information

We want to fill the gap in the given equation with the missing terms.

Step 2. Method to find:

We know that

If an ellipse is given with the following equation.

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

where $a>b$, then it is centred at the origin, the major axis is the y-axis and the parameters $aandb$represent its width: $2a$and its height: $2b$

Step 3. Determining the values of a and b:

From the previous step it is given that $a>b$and then $a^2>b^2$

Therefore, for $\frac{x^2}{25}+\frac{y^2}{9}=1$

Since $25>9$it follows that

$25=5^2=a^2\Rightarrow a=5$and

$9=3^2=b^2\Rightarrow b=3$

Step 4. Determine the major axis:

Since the greater value between $aandb$is under the variable $x$squared it follows that the major axis is the$x-axis.$