Question

I need to find the equation in the standard form of the ellipse when I'm given the focus in the vertex picture included

Answer 1

The equation of the ellipse in the standard form is written in the form,

`(x^2)/(a^2)+(y^2)/(b^2)=`

Given:

`\begin{gathered} Focus=(2,0),\text{ so c=2,c}^2=2^2=4 \\ Vertex=(5,0),\text{ so a=2,}a^2=5^2=25 \end{gathered}`

Therefore, let us evaluate for b^2

`\begin{gathered} c^2=a^2-b^2 \\ 4=25-b^2 \\ b^2=25-4=21 \\ \therefore b^2=21 \end{gathered}`

Let us substitute the values of a^2=25, and b^2=21 into the standard form of the equation

`(x^2)/(25)+(y^2)/(21)=1`

Hence, the answer is

`(x^2)/(25)+(y^2)/(21)=1`