Question 394955
Starting with the standard form for a circle of radius r and center at (h, k):
{{{(x-h)^2+(y-k)^2 = r^2}}}
The center is given as (3, -4) so h = 3 and k = -4. Substitute.
{{{(x-3)^2+(y+4)^2 = r^2}}} Find {{{r^2}}} by substituting the x- and y-coordinates of the given point and solving for r or use the distance formula to find the distance from the center (3, -4) to the point on the circle (-1, -4):{{{d = sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}
{{{(x-3)^2+(y+4)^2 = r^2}}} Substitute x = -1 and y = -4.
{{{(-1-3)^2+(-4+4)^2 = r^2}}} Evaluate.
{{{(-4)^2 = r^2}}}
{{{16 = r^2}}}
Final equation is:
{{{(x-3)^2+(y+4)^2 = 16}}}