Conics how to write the equation of an ellipse given a vertex and focus

The video tutorial explains how to solve a problem involving a vertex and a focus with the center at the origin. It covers plotting the given information, handling irrational numbers, determining the major axis, and calculating the values of A, B, and C using the formula C^2 = A^2 - B^2. The tutorial emphasizes estimation techniques and understanding the relationship between the center, focus, and vertices.

What is the first step in solving the problem of finding the equation of an ellipse?

• Determine the length of the major axis.

• Find the midpoint of the vertices.

• Plot the given information.

• Calculate the distance between the foci.

How can you approximate the value of sqrt(2) when plotting?

• Use the exact value of 1.414.

• Estimate it as 1.5 for simplicity.

• Consider it as 2 for easier calculations.

• Ignore it since it's an irrational number.

What does the position of the focus above the center indicate about the major axis?

• The major axis is horizontal.

• The major axis is vertical.

• The ellipse is a circle.

• The major axis is diagonal.

If the distance from the center to the vertex is 5, what is the value of 'a'?

• 3

• 5

• 7

• 9

What is the final equation of the ellipse given a^2 = 25 and b^2 = 7?

• X^2/9 + Y^2/16 = 1

• X^2/5 + Y^2/3 = 1

• X^2/7 + Y^2/25 = 1

• X^2/25 + Y^2/7 = 1