Ellipses

Question 1

What is the standard form for ellipses?

Answer 1

(x-h)²/ a² + (y-k)²/ b² = 1

Question 2

(x-h)²/ a² + (y-k)²/ b² = 1

What is the meaning of h, k, a, and b?

Answer 2

• (h,k) represents the center of the ellipse
• a represents the horizontal distance from center to edge of ellipse
• b represents the vertical distance from center to edge of ellipse

Question 3

(x-h)²/ a² + (y-k)²/ b² = 1

What determines the major and minor axis?

Answer 3

a and b. Whichever one is greater is the major axis. The smaller one of the two is the minor axis.

Question 4

Purple points on ellipse?

Answer 4

Vertices

Question 5

Vertices of an Ellipse

Answer 5

The endpoints along the major axis.

Question 6

Black points on left and right?

Answer 6

Co-Vertices

Question 7

Co-Vertices of an Ellipse

Answer 7

The endpoints along the minor axis

Question 8

Foci of an ellipse.

How do you find them?

Answer 8

1. Find the difference between the denominators
2. Take the square root of the difference

b² - a² | = c²