Answer:
The standard form of the equation of the ellipse is:
[tex]\frac{(x-4)\placeholder{⬚}^2}{5^2}+\frac{(y-2)\placeholder{⬚}^2}{1^2}\text{ = 1}[/tex]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:
[tex]\frac{(x-h)\placeholder{⬚}^2}{a^2}\text{ + }\frac{(y-k)\placeholder{⬚}^2}{b^2}\text{ = 1}[/tex]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:
[tex](h-2\sqrt{6\text{ }}\text{ -4\rparen}^2\text{ = \lparen a}^2-b^2),(h-9)\placeholder{⬚}^2\text{ = a}^2[/tex]Thus, we have it that:
[tex]\begin{gathered} h\text{ = 4} \\ k\text{ = 2} \\ a\text{ = 5} \\ b\text{ = -1} \end{gathered}[/tex]Thus, we have the standard form as:
[tex]\frac{(x-4)\placeholder{⬚}^2}{5^2}+\frac{(y-2)\placeholder{⬚}^2}{1^2}\text{ = 1}[/tex]
