Question

Radius of the circle with centre $(3,-1)$ and cutting a chord of length $6$ on the line $2x-5y+18=0$ is

• A. $\sqrt{29}$
• B. $\sqrt{38}$
• C. $\sqrt{37}$
• D. $\sqrt{11}$

Answer 1

The correct option is A $\sqrt{29}$

The length of perpendicular form $(3,-1)$ to $2x-5y+18=0$ is

$\left|\frac{2\times 3-5\times (-1)+18}{\sqrt{2^2+5^2}}\right|=\frac{29}{\sqrt{29}}=\sqrt{29}$

Now as circle cuts off an intercept of length $6$,it intercepts at a distance of $3$ on each side form the foot of the perpendicular .

Hence radius of circle is $\sqrt{(\sqrt{29}{)}^2+3^2}=\sqrt{38}$ and equation of circle is

$(x-3{)}^2+(y+1{)}^2=38$