Equation of Ellipse ( Part 1) | Don't Memorise

TL;DR

Learn how to find the equation of an ellipse by using the sum of distances from the focus points and the relationship between the major and minor axis.

Transcript

by now we are quite familiar with the shape ellipse can you tell me what an ellipse is right if we have two fixed points then an ellipse is the set of points such that the sum of the distances from these two fixed points is constant these two fixed points are called the full size of the ellipse we can also draw two axis of symmetry for an ellipse t... Read More

Key Insights

• 😥 An ellipse is defined by the sum of distances from its foci, which is constant for all points on the ellipse.
• ❣️ The equation of an ellipse can be simplified when the center is at the origin and the foci are on the x or y axis.
• 😥 The constant value for any point on an ellipse is equal to the length of the major axis.
• 😑 The relationship between the major and minor axis can be expressed as B^2 = a^2 - C^2.
• ❓ By substituting this relationship into the equation, the simplified equation of an ellipse can be obtained.
• 🍉 The equation of the ellipse can be further simplified by squaring and transposing terms.
• 😥 The equation found is only the potential equation of an ellipse; the converse must be checked to confirm that any point satisfying the equation will lie on the ellipse.

Questions & Answers

Q: What is an ellipse and how is it defined?

An ellipse is a set of points where the sum of distances from two fixed points (foci) is constant. This property makes it different from a circle, which has one fixed center point.

Q: Why are there two possible orientations for an ellipse?

An ellipse can have its foci either on the x-axis or the y-axis. These two scenarios are the only possible orientations that satisfy the conditions of having the center at the origin and the foci on the x or y axis.

Q: What is the constant value equal to for any point on an ellipse?

The constant value for any point on an ellipse is equal to the sum of distances from the foci, which is also equal to the length of the major axis.

Q: How can the equation of an ellipse be simplified?

By using the distance formula and the relationships between the major and minor axis, the equation of an ellipse can be simplified step by step until it is in a relatively simple form.

Summary & Key Takeaways

• An ellipse is defined as the set of points where the sum of distances from two fixed points (foci) is constant.

• The equation of an ellipse can be simplified when the center is at the origin and the foci are on either the x or y axis.

• The sum of distances from the foci is equal to the length of the major axis, and the relationship between the major and minor axis can be used to simplify the equation further.