Equation of the chord of the circle $x^2+y^2-4 x-10 y+25=0$ having mid-point $(1,2)$ is

• A

  $-x+3 y=5$
• Correct answer
  B

  $x+3 y=7$
• C

  $5 x+y=7$
• D

  $3 x+y=5$

Solution

$$ \begin{aligned} & x^2+y^2-4 x-10 y+25=0 \Rightarrow \text { centre }=(2,5) \text { and } \\ & \text { radius }=\sqrt{4+25-25}=2 \end{aligned} $$ Refer figure
Let $\mathrm{M}(1,2)$ be the midpoint of chord Slope of $\mathrm{CM}=\frac{2-5}{1-2}=3$ $\therefore$ Slope of $\mathrm{AB}=\frac{-1}{3}$ Equation of $\mathrm{AB}$ is $(\mathrm{y}-2)=\frac{-1}{3}(\mathrm{x}-1)$ i.e. $\mathrm{x}+3 \mathrm{y}=7$

Hence, the correct answer is option: 'B'.