Answer: The point that lies on the circle is (4) F(-2, 6).
Step-by-step explanation: We are to select the correct point that lies on a circle that that is centred at A(-3, 2) and passes through B(1, 3).
The standard equation of a circle with centre at (g, h) and radius 'r' units is given by
The centre of the given circle is A(-3, 2), so we have
(g, h) = (-3, 2).
Also, the circle passes through the point B(1, 3).
Substituting these values in equation (i), we get
Therefore, the equation of the circle with centre (-3, 2) and radius √17 units is given by
Thus, the required equation of the circle is
Option (1) is C(-1, -2).
We have
So, the point C lies outside the circle.
Option (2) is D(-6, 3).
We have
So, the point D lies inside the circle.
Option (3) is E(-3, -3).
We have
So, the point C lies outside the circle.
Option (4) is F(-2, 6).
We have
So, the point F lies on the circle.
Thus, the point that lies on the circle is F(-2, 6).
Option (4) is correct.