Foci of an ellipse

CONCEPTS

Foci / Focus

• 2 points whose sum of distances from any point on the ellipse is always the same. They lie on the ellipse's major radius

• f² = p² − q² (f = foci, p = major radius or a in the ellipse equation, q = minor radius or b in the ellipse equation)

PRACTICE PROBLEMS

Question 1 What is the foci for the ellipse, x² / 9 + (y – 5)² / 15 = 1?

-- Answer -- (0, 5 + √6), (0, 5 - √6)

f² = p² − q², f = √(√15)² - 3²) = √(15 - 9) = √6

Foci = (0, 5 + √6), (0, 5 - √6)

ACT PRACTICE PROBLEMS

1/1