Points on an ellipse

CONCEPTS

Ellipse Equation

• The center is (h, k), 2a is the transverse or horizontal diameter, and 2b is the vertical diameter

Ellipse Equation and Point on an Ellipse

• Any point that is on a circle can be put into the ellipse equation.

EXAMPLE

• Point (2, 3) is lies on the circle with center (1, 1), a = 2, b = 2 => (2 – 1)²/4 + (3 – 1)²/4 = 1

PRACTICE PROBLEMS

Question 1 Given the ellipse x² / 9 + (y – 5)² / 15 = 1, if point, (3, y) is on the ellipse, what is y coordinate?

-- Answer -- (3, 5)

Stick (3, y) into the ellipse equation

3² / 9 + (y – 5)² / 15 = 1 => 9 / 9 + (y – 5)² / 15 = 1

(y – 5)² = 0, y = 5

ACT PRACTICE PROBLEMS

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