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

1. anonymous

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.

2. Nnesha

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

3. anonymous

|dw:1438730789405:dw|

4. anonymous

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

5. anonymous

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

6. zzr0ck3r

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

7. Nnesha

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

8. Nnesha

yeah same thing

9. Nnesha

Opps nvm

10. -Welp-

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

11. Nnesha

wrong.

12. -Welp-

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

13. -Welp-

halp

14. anonymous

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?