Question

A circle has a center of (5,2) and a radius of 10. Which of the following points will the circle pass through?

Answer 1

equation of the circle with given data is,

`\begin{gathered} (x-5)^2+(y-2)^2=10^2_{} \\ (x-5)^2+(y-2)^2=100 \end{gathered}`
`\begin{gathered} i).(x-5)^2+(y-2)^2=100 \\ (15-5)^2+(12-2)^2 \\ 10^2+10^2 \\ 100+100 \\ 200 \\ it\text{ does not satisfy} \end{gathered}`
`\begin{gathered} ii).(x-5)^2+(y-2)^2=100 \\ (8-5)^2+(7-2)^2 \\ 3^2+5^2 \\ 9+25 \\ 34 \\ it\text{ does not satisfy} \end{gathered}`
`\begin{gathered} iii).(x-5)^2+(y-2)^2=100 \\ (11-5)^2+(-6-2)^2 \\ 6^2+(-8)^2 \\ 36+64 \\ 100 \\ it\text{ satisfies the equation.} \end{gathered}`

Hence, option 3 is correct.