a. Find an equation satisfied by all points that have distance 5 from the point (1,2). Justify your answer using the distance formula?

answers:
Como say: ( x  1)² + (y  2)² = 25

say: A(1; 2).
P(x; y) <=== "All points that have distance 5 from the point A".
Formula (distance between two points):
(Px  Ax)^2 + (Py  Ay)^2 = 5^2.
Hence:
(x  1)^2 + (y  2)^2 = 25.
x^2  2x + 1 + y^2  4y + 4 = 25.
===> x^2 + y^2  2x  4y  20 = 0 (ANSWER).

alex say: circle center (1,2) , Radius = 5

Jeffrey K say: (x1)^2 + (y2)^2 = 5^2
A circle of radius 5 centered at (1,2)

llaffer say: The result is a circle with a radius of 5 with the center being (1, 2).
The general form for an equation of a circle is:
(x  h)² + (y  k)² = r²
Where (h, k) is the center and r is the radius.
Substitute what we know and we have:
(x  1)² + (y  2)² = 5²
(x  1)² + (y  2)² = 25
There is your equation.
