Ellipse and Hyperbola Equations

What is the equation used to find the focal points on an ELLIPSE?

• c² = a² + b²

• c² = a² - b²

• 1/4d

• (x-h)² + (y-k)² = r²

Tags

CCSS.HSG.GPE.A.1

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?

• ( - 2, 2)

• (- 2, 4)

• (2, -2)

• (-2, 1)

Tags

CCSS.HSG.GPE.A.1

What are the equations of the asymptotes for this conic section?16x² - 9y² + 144 = 0

• y = (4/3)x; y = -(4/3)x

• y = (3/4)x; y = -(3/4)x

• y = 0; x = 0

• y = (16/9)x; y = -(16/9)x

Name the conic section and find the center.25x² + 9y² + 50x - 36y - 164 = 0

• ellipse; C(-1, 2)

• hyperbola; C(-1, -2)

• ellipse; C(-2, 4)

• ellipse; C(1, 2)

Tags

CCSS.HSG.GPE.A.1

Name the conic section and determine the vertices.9x² - 4y² - 54x-16y - 79 = 0

• hyperbola; (3, 4), (3, -8)

• hyperbola; (7, -2), (-1, -2)

• hyperbola; (9,  -2), (-3, -2)

• hyperbola; (3, 2), (3, -6)

This equation describes what kind of graph?

• Vertical Hyperbola

• Vertical Ellipse

• Horizontal Hyperbola

• Horizontal Ellipse

Determine the equation of the hyperbola.

What is the "a" value of this hyperbola?

• 5

• 6

• 3

• 4

• 7.5

What is the "b" value of this hyperbola?

• 3

• 5

• 4

• 6

• 7.5

What is the "c" value of this hyperbola?

• 5.83

• 4.45

• 3.34

• 6.5

• 7.25