Determine whether each point lies on the circle. Then use symmetry to determine another point on the circle. Circle K has its center at (0,0) and a radius of 4. Point N is at (3,7).

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Given:

Circle K has its center at (0,0) and a radius of 4.

Point N is at .

To find:

To check whether the point N lies on the circle or not. Then find the other point using symmetry.

Solution:

The standard form of a circle is

      ...(i)

where, (h,k) is center and r is radius.

Circle K has its center at (0,0) and a radius of 4.  Putting h=0, k=0 and r= 4 in (i), to get the equation of circle K.

      ...(ii)

To check the point , put x=3 and in (ii).

This statement is true. So. option lies on the circle K.

According to the symmetry about the origin, if (x,y) lies on the graph then (-x,-y) also lies on that graph.

Since the center of the circle is origin, therefore, it is symmetrical about the origin.

Thus, point must be on the circle K.

Therefore, the another point on the circle K is .

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153