If a circle with radius 2.5 units passes through the points $(2,3)$ and $(5,7)$, then its centre is

Question

Aicharya · Accepted Answer

Let centre of the circle be $c(x, y)$.

Here, $C A$ and $C B$ both represents the radius of the circle. So, it will be equal. Then, $\quad C A=C B$ $ \begin{array}{cc} \Rightarrow & C A^2=C B^2 \\ \Rightarrow & (5-x)^2+(7-y)^2=(2-x)^2+(3-y)^2 \\ \Rightarrow & 25+x^2-10 x+49+y^2-14 y \\ & =4+x^2-4 x+9+y^2-6 y \\ \Rightarrow & 74-13=6 x+8 y \\ \Rightarrow & 6 x+8 y=61 \end{array} $ This equation is satisfied by the coordinates given in option (d)

If a circle with radius 2.5 units passes through the points $(2,3)$ and $(5,7)$, then its centre is

Solution