7/25/2019 Extra Question Conics

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Lesson 10Conics Sections

Extra Questions

1. An ellipse has vertices (0, 9) and foci (0, 5). Find the standard-form equation of the

ellipse, its directrices and eccentricity.

2. The hyperbola

is shifted horizontally and vertically to obtain the

hyperbola()

()

. Find the foci, vertices, directrices, asymptotes andeccentricity of the new hyperbola.

3. Using the process of completing the square, determine the conic form represented by

the equation .

4.

The ellipse

is shifted 3 units to the left and 2 units down to generate

the ellipse

.(a)Find the foci, vertices and center of the new ellipse.

(b)

Plot the new foci, vertices and center, and sketch the new ellipse.

5. Find the ellipses standard-form equation given the following information.

Foci: (, 0)Vertices: (2, 0)

6.

Find the hyperbolas standard-form equation given the following information.

Eccentricity: 2

Vertices: (2, 0)

7. Determine whether the equation represents aparabola, ellipse or hyperbola.

Answers

1.

; Directrices,

; Eccentricity,

2. New center (-5, 1) ; New vertices (-1, 1) & (-9, 1) ; New Foci (-10, 1) & (0, 1)

Asymptotes, and

; Eccentricity,

;

Directrices, and

3.

Parabola, shifted 2 units left and 2 units up.

4. New center (-3, -2) ; new foci (-3, -6) & (-3, 2) ; new vertices (-3, -7) & (-3, 3) ;

New co-vertices (-6, -2) & (0, -2)

5.

6.

7.

Hyperbola