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: (x-1)^2 + (y-2)^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.
-