Question

Graph the following ellipse and state its center and vertices

Answer 1

Step-by-step explanation:

Given;

We are given the following equation of an ellipse;

`9x^2+36x+4y^2-8y=-4`

Required;

We are required to graph the ellipse and state its center and vertices.

Step-by-step solution;

`\begin{gathered} Re-write\text{ }in\text{ }standard\text{ }form: \\ ((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 \end{gathered}`

We now have;

`\begin{gathered} Our\text{ }ellipse\text{ }is\text{ }in\text{ }the\text{ }form: \\ ((x-(-2)^2)/(4)+((y-1)^2)/(9)=1 \\ Hence: \\ \\ ((x+2)^2)/(2^2)+((y-1)^2)/(3^2)=1 \end{gathered}`

With the center given as (h, k), we now have

`Center=(-2,1)`

Also,

`a=2,b=3`

Using a graphing tool, the graph would now appear as follows;

The vertices as shown in the graph are found at the point;

`\begin{gathered} (h,k+b) \\ (h,k-b) \\ Hence: \\ (-2,1+3),(-2,1-3) \\ \\ Vertices=(-2,4),(-2,-2) \end{gathered}`

Therefore,

ANSWER:

`\begin{gathered} Center=(-2,1) \\ \\ Vertices)=(-2,4),(-2-2) \end{gathered}`