Question

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. $(4,8)$

Answer 1

The correct option is A $(-2,12)$

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 $=\sqrt{{(-6)}^2+{\left(8\right)}^2}=\sqrt{36+64}=\sqrt{100}=10$
The given choices can be plotted in the
co-ordinate plane 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