Question

The center of the circle whose equation is (x - 2)2 + (y + 4)2 = 25 is?

Answer 1

do you know the distance formula?
\[d=\sqrt{(x-x_1)^2+(y-y_1)^2}\]

I'm going to write the formula for distance square:
\[d^2=(x-x_1)^2+(y-y_1)^2 \]


Say you choose a point on the circle (x,y). Say you draw a straight line from that point to the center of the circle. Is that length the same as if you chose another point on that same circle and drew a straight line from that point to the center?

Basically I'm asking you what do you think (x1,y1) have to be in order for the equation\[d^2=(x-x_1)^2+(y-y_1)^2 \] to be the equation of a circle in center-radius form.

Answer 2

A circle has this formula\[(x-x_c)^2+(y-y_c)^2=r^2\]Where \[(x_c,y_c)\] is the center of the circle.
if\[x_o=2~~and~~y_o=-4\] So the center of this circle is\[\boxed{C=(2,-4)}\]