exercise module 8 conic

EXERCISE: CONIC SECTIONS

1.

Label the following graphs with: Centre as C Focus as F Latus rectum as d Minor vertices as V3 and V4 wherever appropriate.

, , , ,

Vertex as V , Radius as r , Major vértices as V1 and V2 Foci as F1 and F2

,

y

y

y

x

x

x

2.

State the equation of circle centered at ( –3, 1) and diameter of 4 units.

3.

Find the coordinate of center and calculate the radius for 4x 2 − 40x + 4y 2 + 4y = −93 .

Then, sketch the graph.

4.

Given the equation of parabola:

( y − 2 )2 = 8 ( 2 − x ) a) b) c) 5.

Locate the vertex, focus and the line of symmetrical axis.

Calculate the length of latus rectum.

Sketch the graph.

Construct the equation of an ellipse with the following properties: a=8

;

major axis, y = -1

;

lines of latus rectum are at x = 0 and x = 8.

Then, sketch the graph.

6.

Based on the following information: Line of major axis, y = - 3

Length of major axis = 1 unit 11 Length of latus rectum = ¼ unit , y-intecept at − 4 Name the conic section and construct the equation.

7.

,

Circumference of a round trampoline is 40 in . Construct the standard equation of circle that represent the shape of the trampoline.

ALL RIGHTS RESERVED MOOC MAT099

1

EXERCISE: CONIC SECTIONS

8.

The arch of a bridge forms the top half of an ellipse. The arch is 6m above the 20m wide river. a) Write an equation for the ellipse in which the water level coincides with the major axis. b) A water depth marker is placed at the focus of the ellipse; find the distance of the marker from the center.

9.

A parabolic lens focuses light onto a focal point 3 cm from vertex of the lens. How wide is the lens 0.5 cm from the vertex?

ANSWER: 2.

( x + 3)

2

+ ( y − 1) = 4 2

3. C=(5, –½ ); r = √2 4. a) V = (2, 2); F = (0, 2); y = 2 b) 8 units 5.

(x − 4)2 + (y + 1)2 64

48

=1

6. Ellipse, 4x 2 + 16 ( y + 3 ) = 1 2

7. x2 + y2 = 400 if 8. a) b)

C ( 0,0 )

x2 y2 + =1 100 36

8m

9. 4.899 cm

ALL RIGHTS RESERVED MOOC MAT099

2