Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?

C(-1, -2)

D(-6, 3)

E(-3, -3)

F(-2, 6)

Sagot :

naǫ
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) - the coordinates of the center
r - the radius

[tex]\hbox{the center: } A(-3,2) \\ h=-3 \\ k=2 \\ \\ \hbox{the equation:} \\ (x+3)^2+(y-2)^2=r^2 \\ \\ \hbox{the circle passes through B(1,3)} \\ x=1 \\ y=3 \\ \Downarrow \\ (1+3)^2+(3-2)^2=r^2 \\ 4^2+1^2=r^2 \\ 16+1=r^2 \\ 17=r^2 \\ \\ \hbox{the equation is:} \\ (x+3)^2+(y-2)^2=17[/tex]

Plug the coordinates of the points into the equation and check:
[tex]C(-1,-2) \\ (-1+3)^2+(-2-2)^2=17 \\ 2^2+(-4)^2=17 \\ 4+16=17 \\ 20=17 \\ not \ true \\ \\ D(-6,3) \\ (-6+3)^2+(3-2)^2=17 \\ (-3)^2+1^2=17 \\ 9+1=17 \\ 10=17 \\ not \ true[/tex]

[tex]E(-3,-3) \\ (-3+3)^2+(-3-2)^2=17 \\ 0^2+(-5)^2=17 \\ 25=17 \\ not \ true \\ \\ F(-2,6) \\ (-2+3)^2+(6-2)^2=17 \\ 1^2+4^2=17 \\ 1+16=17 \\ 17=17 \\ true[/tex]

The answer is F(-2,6).
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.