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
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

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

the answer is c hope it

step-by-step explanation: