Question 1159152


Which is the equation of a circle that passes through ({{{2}}},{{{2}}}) and is centered at ({{{5}}},{{{6}}})


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


Answers:

A. {{{(x-6)^2 + (y-5)^2=25}}}=>{{{h=6}}}, {{{k=5}}} -> not your answer

B. {{{(x-5)^2 + (y-6)^2=5}}}=>{{{h=5}}}, {{{k=5}}} -> might be your answer
check if this a circle that passes through ({{{2}}},{{{2}}})

{{{(2-5)^2 + (2-6)^2=5}}}
{{{3^2 + (-4)^2=5}}}
{{{9 + 16=5}}}
{{{25<>5}}}=> a circle does not passes through ({{{2}}},{{{2}}})

so, B. is not your answer either


C. {{{(x+5)^2 + (y+6)^2=25}}}=>{{{h=-5}}}, {{{k=-6}}} -> not your answer


D. {{{(x-5)^2 + (y-6)^2=25}}}=>{{{h=5}}}, {{{k=6}}} -> might be your answer

check if this a circle that passes through ({{{2}}},{{{2}}})

{{{(2-5)^2 + (2-6)^2=25}}}
{{{3^2 + (-4)^2=25}}}
{{{9 + 16=25}}}
{{{25=25}}}=> true=>this is a circle that passes through ({{{2}}},{{{2}}})

and have a center at ({{{5}}},{{{6}}})

so, your answer is {{{D}}}.