Ellipse Properties and Calculations

What is the orientation of the major axis in an ellipse where a > b?

• Diagonal

• Horizontal

• Vertical

• None of the above

In the ellipse equation x^2/a^2 + y^2/b^2 = 1, what does 'a' represent?

• Center of the ellipse

• Focal length

• Semi-major axis

• Semi-minor axis

What is the constant sum of distances from any point on an ellipse to its foci?

• 2b

• a

• 2a

• b

Which axis do the foci of an ellipse lie on when a > b?

• Vertical axis

• Horizontal axis

• Both axes

• Neither axis

Which property of an ellipse is often used as its definition?

• The sum of distances to the foci is constant

• The area is constant

• The perimeter is constant

• The diameter is constant

How can the focal length of an ellipse be calculated?

• a - b

• Square root of (a^2 - b^2)

• Square root of (b^2 - a^2)

• a + b

What is the semi-minor radius of an ellipse with b^2 = 4?

• 2

• 4

• Square root of 4

• 1

What is the focal length of an ellipse with a = 3 and b = 2?

• Square root of 3

• 5

• Square root of 5

• 1

What is the center of the ellipse given by the equation (x-1)^2/9 + (y+2)^2/4 = 1?

• (2, -1)

• (0, 0)

• (1, -2)

• (-1, 2)

How do you find the coordinates of the foci for an ellipse centered at (1, -2)?

• Add and subtract the focal length from the y-coordinate

• Add the focal length to both coordinates

• Subtract the focal length from both coordinates

• Add and subtract the focal length from the x-coordinate