Graph each ellipse and give the location of its foci. x²/25 + ...

Question

Graph each ellipse and give the location of its foci. x²/25 + (y -2)² /36= 1

Accepted Answer

Wrap the given ellipse and indicate it both sign where equation is X squared over nine plus Y minus three squared, divided by 49 is equals to one. Now, the general form of new lips is given by X minus H squared, divided by A squared plus Y minus K squared divided by B squared as equals to one where the point H K is our center. Now to determine the equation of our lips, sorry graph of our lips rather, we need to look at our A squared and our B squared since B squared is under the Y squared and it's larger than our A squared. This is gonna be a vertically oriented the lips. This is because our B will be greater than A where A, Since a squared is nine or a will be three RB within B seven. Let's find the end points of outward lips. As your vertical. We all take the equations each K plus B and H K minus B to find the end points of our lips at least in the right direction. R center H K, then We can determine will be zero and three. Now our end points, B zero three plus seven and 0 3 -7, Which gives us 0 10 & 0 -4. Now, we have the end points, we can find the focus with the sign. So you have multiple focus. We will take the equations H K plus C and H K minus C. Where C is the linear eccentricity of our ellipse to find C, we take the equation square root B squared minus A squared because we know B is larger than A, we will put B squared first C is equal to the square root of 49 -9 or C is a squared of 40. We can then simplify the square of 40 that simplifies the two squares of tin. We can then write our focus as zero three plus two squares of 10, N 03 -2 Squared to 10. We can simplify that we will get zero, negative 3.325 and 9.325. If we were to change them into decimals, if we look at our possible graphs, we want a vertical ellipse with all four points that we found. This corresponds with. Answer C OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each ellipse and give the location of its foci. x²/25 + (y -2)² /36= 1

Key Concepts

Standard Form of an Ellipse

Identifying the Major and Minor Axes

Finding the Foci of an Ellipse

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