Question

Equation of circle whose centre is (3,-1) and which cut of an intercept of length 6 unit from the line 2x-5y+18=0 is:

Answer 1

REF.Image.

$\perp r$ distance of line $2x-5y+18=0$ from point

(3,-1)

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

distance

$\perp r$ of (h,k)from

$ax+by+c=0$ is

$\left|\frac{ah+bk+c}{\sqrt{a^2+b^2}}\right|$

Thus $r^2=h^2+3^2$ [Pythagoras theorem in $△OAC]$

$r^2=29+9$

$r^2=38$

Thus $e{q}^n$ of circle is $(x-3{)}^2+(y+1{)}^2=38.$