Answer:

Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,

let,
thus substitute:

simplify addition:

simplify division:

so the centre of the circle is <u>(</u><u>4</u><u>,</u><u>-</u><u>4</u><u>)</u>
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is

simplify which yields:

recall the equation of circle

we acquire that,
therefore substitute:

simplify:

and we are done!
also refer the attachment
(the graph is web resource of desmos)