Question

The ellipse with x-intercepts (5,0) and (-5,0); y-intercepts (0,3) and (0,-3)

Answer 1

Given an ellipse with following parameters

`\begin{gathered} x-\text{intercepts }\Rightarrow(5,0),(-5,0) \\ y-\text{intercepts}\Rightarrow(0,3),(0,-3) \end{gathered}`

The general formula of an ellipse is given as

`((x-h)^2)/(b^2)+((y-k)^2)/(a^2)=1`

The coordinate of the center is (h, k )

The vertices on x-axis is at (b, 0) and (-b , 0)

The vertices on y-axis is at (0, a) and (0, -a)

We can deduce from the parameters provided that

`\begin{gathered} h=0,k=0 \\ (b,0)=(5,0)\Rightarrow b=5 \\ (0,a)=(0,3)\Rightarrow a=3 \end{gathered}`

Thus the ellipse equation can be calculated as

`\begin{gathered} ((x-0)^2)/(5^2)+((y-0)^2)/(3^2)=1 \\ (x^2)/(25)+(y^2)/(9)=1 \end{gathered}`

Hence, the ellipse equation is

`(x^2)/(25)+(y^2)/(9)=1`