Question

A circle passes through the points $(-1,3)$ and $(5,11)$ and its radius is $5$. Then its centre is:

• A. $(-5,0)$
• B. $(-5,7)$
• C. $(2,7)$
• D. $(5,0)$

Answer 1

The correct option is C $(2,7)$

Distance between given points

$=\sqrt{(5-(-1){)}^2+(11-3{)}^2}$

$=\sqrt{36+64}$

$=10$

Since distance between the given points is twice the radius and they also lie on circle,

So, they must be diametric ends.

Thus, center of circle,

$\to (\frac{-1+5}{2},\frac{3+11}{2})$

$\to (2,7)$

Hence, (C) is the correct answer.