Question 965562

What is the equation of a circle with a center at (-2, 4) and a radius of 4?

recall the formula: {{{(x-h)^2 + (y-k)^2 = r^2}}} where {{{h}}} and {{{k}}} are {{{x}}} and {{{y}}} coordinates of the center, and {{{r}}} is a radius 

A. 

{{{(x-2)^2 + (y+4)^2 = 16}}}...here we see that {{{h=2}}},{{{k=-4}}} (a center at ({{{2}}},{{{ -4}}})), and {{{r=4}}} 

B. 

{{{(x+2)^2 + (y-4)^2 = 16}}}...here we see that {{{h=-2}}},{{{k=4}}} (a center at ({{{-2}}},{{{ 4}}})), and {{{r=4}}} 

C. 

{{{(x+2)^2 - (y-4)^2 = 16}}}...here we see that {{{h=-2}}},{{{k=4}}},but this is a hyperbola, not a circle

D. 

{{{(x-2)^2 - (y+4)^2 = 16}}}........this is a hyperbola, not a circle


so, the equation of a circle with a center at ({{{-2}}},{{{ 4}}}) and a radius of {{{4}}} is  {{{(x+2)^2 + (y-4)^2 = 16}}}

and your answer is B.


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(-2,4,.12),circle(-2,4,4),locate(-2,4,C(-2,4)),
 graph( 600, 600, -10, 10, -10, 10, 0)) }}}