Question

The question asks, "Find the equation of the ellipse with the following properties.

Answer 1

Answer:

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

Step-by-step explanation:

Equation of ellipse is of form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ where $(a,0) , (-a,0)$ are the x-intercepts and $(0,b) , (0,-b)$ are the y-intercepts . If $a > b$ then it is a horizontal ellipse and if $a < b$ then it is a vertical ellipse .

For horizontal axis ,

Here, $(a,0) , (-a,0)$ are known as the vertices of ellipse and $(0,b) , (0,-b)$ are the co-vertices of ellipse .

Horizontal axis is known as the major axis and vertical axis is known as the minor axis .

Here, x-intercepts are $(5,0) , (-5,0)$ , take a = 5

y-intercepts are $(0,3) , (0,-3)$ , take b = 3

As $a > b$ , it is a horizontal ellipse .

On putting a = 5 and b = 3 , we get equation as

$\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1$

Answer 2

Answer:

x^2 / 25 + y^2 / 9 = 1

Step-by-step explanation:

The major axis is along the x axis and the minor axis is on the y axis.

Major axis = 2a =  5--5 =10 so a = 5 and a^2 = 25.

Similarly b^2 = 3^2 = 9.