106k views
1 vote
I need help with step by step on this problem with formulas

I need help with step by step on this problem with formulas-example-1
User Talvalin
by
8.3k points

1 Answer

3 votes

Answer:

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}

User Manish Basdeo
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories