Question

Which equation represents a circle centered at (3,5) and passing through the point (-2,9)?

Answer 1

Given

centered at (3 , 5) and passes through (-2 , 9)

Find

Equation of the circle

Explanation

an equation of the circle is given by

$(x-h)^2+(y-k)^2=r^2$

where (h ,k) be the center and r be the radius

we need to find the radius of circle.

here , we use distance formula to find radius.

points (3 ,5) and (-2 , 9)

$\begin{gathered} d=\sqrt{(-2-3)^2+(9-5)^2} \\ d=\sqrt{25+16} \\ d=\sqrt{41} \end{gathered}$

so , equation of circle is

$\begin{gathered} (x-3)^2+(y-5)^2=(\sqrt{41})^2 \\ (x-3)^2+(y-5)^2=41 \end{gathered}$

Final Answer

Hence , the correct option is D