Question

"What is the equation of the circle with center (3,5) that passes through the point (-4,10)?"
^How do I solve this?

Answer 1

Use the distance formula first to find the radius.\[\huge d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]

After you found the radius, use the center and the radius to form the standard equation of a circle.

Answer 2

or you can use equation of the circle
replace (h,k) for center points
and x , y by the point they gave you
solve for r

Answer 3

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 5}})\quad
% (c,d)
&({\color{red}{ -4}}\quad ,&{\color{blue}{ 10}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 4

find the radius
use the center (h,k) as Nnesha indicated on the previous posting
and plug them in
\(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{purple}{ r}}^2

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
radius={\color{purple}{ r}}\)

Answer 5

@Nnesha solving for r in the standard equation gives the distance formula :)

Answer 6

\[\huge\rm (\color{blue}{x}-\color{reD}{h})^2+(\color{blue}{y}-\color{reD}{k})^2=r^2\] \[\color{blue}{(-4,10)}\] \[\color{reD}{(3,5)}\]
plugin values solve for r

Answer 7

yeah same thing

Answer 8

Opps nvm

Answer 9

"plugin values solve for r " I tried it and got 24. That doesn't seem right.

Answer 10

wrong.

Answer 11

=(x-3)^2 + (y-5)^2=226?

Answer 12

halp

Answer 13

The left hand side of your equation of the circle is correct. However, the right hand side (226) is incorrect. Did you use the distance formula above to find the radius?