how to solve my Q1 for exapmle of past paper

Question

1.1. 1.1.1. Sketch the graph of (x^2/72) - (y^2/32) = (1/2) 1.2. What is the domain of the graph in 1.1. 1.3. Is the graph in Q 1.1 symmetrical about both axes? 1.4. Does the graph in Q1.1 represent a function or relation? 1.2. Sketch the graph of x = - square root of (20-y^2) 1.3. Skecth and indicate the area enclosed by the graph of y=cos x. The x-axis, x=0 and x= (pie/2). Also undicate the representative strip to be used to calculate the area of the enclosed area.

Answer 1

1.1.

The equation is .

Write equation in standard form .

Vertices: (a, 0) = (6, 0) and (-a, 0) = (-6, 0)

Co-vertices: (0, b) = (0, 4) and (0, -b) = (0, -4).

Equations of asymptotes: .

Graph :

 

(1.2).

Observe the graph, the domain of the graph is (-∞, -6] U [6, ∞).

Answer 2

(1.3).

Graph :

Yes, the graph is the symmetrical about the both axis.

x-aixs: (x, y) = (8.5, 4) <----> (x, -y) = (8.5, -4).

y-aixs: (x, y) = (8.5, 4) <----> (-x, y) = (-8.5, 4).

Answer 3

(1.4).

Vertical Line Test for Functions:

This is not a graph of y as a function of x, because you can find a vertical line that intersects the graph twice. That is, for a particular input  x, there is more than one output y.

Answer 4

2).

The equation is x = - square root of (20-y^2) and its graph is

Answer 5

(3).

The equation is x = - square root of (20-y^2) and its graph is

Find the area :

.