Find the equation of an ellipse give foci and end points of major axis

The video tutorial explains how to determine the center of an ellipse using its foci, and how to identify the major and minor axes. It covers the ellipse equation, focusing on the variables A, B, and C, and demonstrates how to calculate these values. The tutorial concludes with writing the final equation of the ellipse.

How is the center of an ellipse determined using its foci?

• By calculating the average of the foci coordinates

• By finding the midpoint between the foci

• By measuring the distance from one foci to the other

• By using the distance formula on the foci

What lies on the major axis of an ellipse?

• The foci, center, and vertices

• Only the center

• Only the foci

• The vertices and co-vertices

What is the formula for a horizontal ellipse?

• X^2/a^2 + Y^2/b^2 = 1

• X^2/b^2 + Y^2/a^2 = 1

• X^2/a^2 - Y^2/b^2 = 1

• Y^2/a^2 + X^2/b^2 = 1

What does the variable 'A' represent in the ellipse formula?

• Distance from foci to vertices

• Distance from center to vertices

• Distance from center to co-vertices

• Distance from center to foci

How is the value of B determined in the ellipse equation?

• By measuring the distance from center to foci

• By using the formula C^2 = a^2 - b^2

• By measuring the distance from center to vertices

• By using the formula C^2 = a^2 + b^2

What is the final equation of the ellipse given in the tutorial?

• (X - 3)^2/5 + (Y + 4)^2/9 = 1

• (X + 3)^2/5 + (Y - 4)^2/9 = 1

• (X - 3)^2/9 + (Y + 4)^2/5 = 1

• (X + 3)^2/9 + (Y - 4)^2/5 = 1

What is the relationship between C, A, and B in an ellipse?

• C = a + b

• C^2 = a^2 + b^2

• C = a - b

• C^2 = a^2 - b^2