Answer:
Part 1) False
Part 2) False
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to

where
(h,k) is the center and r is the radius
In this problem the distance between the center and a point on the circle is equal to the radius
The formula to calculate the distance between two points is equal to
Part 1) given the center of the circle (-3,4) and a point on the circle (-6,2), (10,4) is on the circle.
true or false
substitute the center of the circle in the equation in standard form

Find the distance (radius) between the center (-3,4) and (-6,2)
substitute in the formula of distance
The equation of the circle is equal to


Verify if the point (10,4) is on the circle
we know that
If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle
For x=10,y=4
substitute


-----> is not true
therefore
The point is not on the circle
The statement is false
Part 2) given the center of the circle (1,3) and a point on the circle (2,6), (11,5) is on the circle.
true or false
substitute the center of the circle in the equation in standard form

Find the distance (radius) between the center (1,3) and (2,6)
substitute in the formula of distance
The equation of the circle is equal to


Verify if the point (11,5) is on the circle
we know that
If a ordered pair is on the circle, then the ordered pair must satisfy the equation of the circle
For x=11,y=5
substitute


-----> is not true
therefore
The point is not on the circle
The statement is false