Equations of circles Use the results of Exercise to describe and graph the following circles.

r2 + 2r(cos θ − 3 sin θ) = 4

Solution 72E

Step 1:

In this problem;

We have to describe and graph of the circle

We know that the polar equation represents a circle of radius ‘R’ centered at ( a, b).

Consider ,

By , using the above result represents a circle.

So , here a = -1, b = 3 , and = 4

= 4

= 4

= 4

+ 4 = 14

.

Therefore ,

represents a circle of radius ‘’ centered at ( -1, 3).

Step 2:

In another way ; Consider ,

We know that ,the relation between cartesian (x, y) and polar coordinates ( r , is ;

x = r cos(, y = r sin(

Therefore , .

By using this results , we get ;

+2x -6y = 4

+2(x) +

= 4+

represents a circle with center (-1 ,3) , and radius ‘’.

Note ; represents a circle with center ( a, b) , and radius ‘r’. |