Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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 visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.