Q22 Equation of an ellipse from the graph

TL;DR

Understanding and finding the equation of an ellipse through analyzing its graph and center coordinates.

Transcript

here were given the graph of this ellipse and welcome to find question for this and to do that we had to first recordist in the form of the ellipse we have the parentheses X minus H inside goes to a second power over a square and then we add for the ellipse situation we have the plus in the middle the second Paris parentheses y minus K inside in th... Read More

Key Insights

• 🇭🇰 The equation of an ellipse is (X-H)^2/a^2 + (Y-K)^2/b^2 = 1, where (H,K) is the center.
• 😃 'a' in the ellipse equation measures horizontal distances, while 'b' represents vertical distances.
• 🚥 To find 'a,' count the horizontal movements from the center to the ellipse.
• 🔄 Determining 'b' involves counting the vertical movements from the center to the ellipse.
• 🆘 Values of 'a' and 'b' help in formulating the complete equation of the ellipse.
• 📈 Understanding the graph and center coordinates are crucial for finding the equation of an ellipse.
• 😃 Vertical and horizontal stretches or compressions are reflected in 'a' and 'b' values.

Questions & Answers

Q: How is the equation of an ellipse represented?

The standard form of an ellipse equation is (X-H)^2/a^2 + (Y-K)^2/b^2 = 1, where (H,K) is the center of the ellipse.

Q: How do you determine the values of 'a' and 'b' for an ellipse?

To find the values of 'a' and 'b,' count the number of movements from the center in the horizontal and vertical directions to the ellipse, respectively.

Q: What does 'a' represent in the equation of an ellipse?

'a' indicates the distance from the center to the points on the ellipse horizontally, representing the ellipse's horizontal stretch or compression.

Q: How is the value of 'b' calculated for an ellipse?

'b' corresponds to the vertical distance from the center to the ellipse, showing the vertical stretch or compression of the ellipse.

Summary & Key Takeaways

• Explaining the equation of an ellipse, (X-H)^2/a^2 + (Y-K)^2/b^2 = 1, where (H,K) is the center.

• Determining the values of 'a' and 'b' by counting movements from the center to the ellipse in the horizontal and vertical directions.

• Applying the found values of 'a' and 'b' to form the complete equation of the ellipse.