Find the equation of the circle whose centre is at `(3,-1)` and which cuts off a chord of length `6u n i t s` on the line `2x-5y+18=0.`

Explanation

Given centre of the circle is `(3,-1)`

Now, OP=`abs((6+5+18)/(sqrt(4+25)))=29/(sqrt(29))=sqrt(29)`
In `DeltaOPB, OB^(2)=OP^(2)+PB^(2)` [`becauseAB=6rArrPB=3`]
`rArr OB^(2)=29+9rArrOB^(2)=38`
So, theradius of circle is `sqrt38`
`therefore` Equation of the circle with radiusr=`sqrt(38)` and centre `(3,-1)` is
`rArr (x-3)^(2)+(y-1)^(2)=38`
`rArr x^(2)-6x+9+y^(2)+2y+1=38`
`x^(2)+y^(2)-6x+2y=28`