question_answer

A circle whose center is at (-6, 8) passes through the origin which of the following points are not on the circle?

A)  (-2, 12)                  

B)  \[(-16,8)\]

C)  (-6,-2)                 

D)         (4 , 8)

Correct Answer: A

Solution :

 To get the answer, we first draw the diagram as described. As the circle passes through the origin, the line joining origin and center of the circle is the radius of the circle. Observing the figure, we get a right triangle with radius as the hypotenuse of this triangle. \[\therefore \]   Radius \[=\sqrt{{{(-6)}^{2}}+{{(8)}^{2}}}\]                 \[=\sqrt{36+64}=\sqrt{100}=10\] The given choices can be plotted in the co-ordinate piano as follows.                 The points \[(4,\,\,8)\] and \[(-16,\,\,8)\] are easy to plot as they are 10 units to the right and left respectively of the center of the circle. Hence, they are on the circle. Again, plotting point \[(-6,-2)\] 10 units below the center of the circle. Hence, again this point is on the circle. Again, taking point, \[(-12,0),\] we can again apply the Pythagoras theorem to get the distance 10 from the center. The remaining point, i.e. \[(-2,12)\] does not lie on the circle.