Respuesta :
Given:
Circle K has its center at (0,0) and a radius of 4.
Point N is at [tex](3,\sqrt{7})[/tex].
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
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(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.
[tex](x-0)^2+(y-0)^2=4^2[/tex]
[tex]x^2+y^2=16[/tex] ...(ii)
To check the point [tex]N(3,\sqrt{7})[/tex], put x=3 and [tex]y=\sqrt{7}[/tex] in (ii).
[tex](3)^2+(\sqrt{7})^2=16[/tex]
[tex]9+7=16[/tex]
[tex]16=16[/tex]
This statement is true. So. option [tex]N(3,\sqrt{7})[/tex] 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 [tex]P(-3,-\sqrt{7})[/tex] must be on the circle K.
Therefore, the another point on the circle K is [tex]P(-3,-\sqrt{7})[/tex].
