Question

What is the equation of the following graph?

Answer 1

`\frac{ {(x - 5)}^(2) }{ 1 } + \frac{ {(y - 7)}^(2) }{ 9} = 1`

Explanation:

The graph is an ellipse centered at (5,7).

The length of the major axis is 2a=10-4

`\implies 2a = 6`

`a = 3`

The length of the minor axis 2b=6-4

`\implies \: 2b = 2`

`b = 1`

The equation is given by

`\frac{( {x - h)}^(2) }{ {b}^(2) } + \frac{ {(y - k)}^(2) }{ {a}^(2) } = 1`

We substitute to get:

`\frac{ {(x - 5)}^(2) }{ {1}^(2) } + \frac{ {(y - 7)}^(2) }{ {3}^(2) } = 1`