Question

I need help with step by step on this problem with formulas

Answer 1

The standard form of the equation of the ellipse is:

`\frac{(x-4)\placeholder{⬚}^2}{5^2}+\frac{(y-2)\placeholder{⬚}^2}{1^2}\text{ = 1}`

Step-by-step explanation:

Here, we want to find the equation of the ellipse

The general form equation of an ellipse with center (h,k) and length of the semi-major and semi-minor axes is as follows:

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

where (h,k) represents the coordinates of the center and (a,b) represents the lengths of the semi-major and semi-minor axes

We have h = 4 and k = 2

Using the equation that takes in ellipse properties, we have it that:

`(h-2\sqrt{6\text{ }}\text{ -4\rparen}^2\text{ = \lparen a}^2-b^2),(h-9)\placeholder{⬚}^2\text{ = a}^2`

Thus, we have it that:

`\begin{gathered} h\text{ = 4} \\ k\text{ = 2} \\ a\text{ = 5} \\ b\text{ = -1} \end{gathered}`

Thus, we have the standard form as:

`\frac{(x-4)\placeholder{⬚}^2}{5^2}+\frac{(y-2)\placeholder{⬚}^2}{1^2}\text{ = 1}`