Question

Analyze the equation and graph it.

Answer 1

Step 1:

The polar equation is .

Convert the polar equation into standard form of the polar equation .

Take out 3 as common from the denominator.

Now compare the above equation with standard form:  and .

The eccentricity of the conic equation is .

As eccentricity , the given conic section is a hyperbola.

 

Answer 2

Contd....

Step 2:

The hyperbola equation is .

Directrix is perpendicular to the polar axis x = -p.

Directrix is perpendicular to the polar axis at a distance units to the left of the pole.

The value in the numerator is .

Substitute in .

Then the directrix is perpendicular to the polar axis at a distance units to the left of the pole.

The directrix is .

Answer 3

Contd....

Step 3:

Construct a table for different values of .

Graph:

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points to a smooth curve.

Answer 4

Contd....

Solution :

The eccentricity of the conic equation is .

The given conic section is a hyperbola.

The directrix of the hyperbola is .

 The vertices are and .