Given circle is x2+y2−16=0 Eqn of chord say AB of given circle is 3x+y+5=0 Equation of required circle is x2+y2−16+λ(3x+y+5)=0 ⇒x2+y2+(3λ)x+(λ)y+5λ−16=0 Centre C=(
−3λ
2
,
−λ
2
). If line AB is the diameter of circle (1), then C(
−3λ
2
,
−λ
2
) will lie on line AB. i.e. 3(
−3λ
2
)+(
−λ
2
)+5=0 ⇒−
9λ−λ
2
+5=0⇒λ=1 Hence, required eqn of circle is x2+y2+3x+y+5−16=0 ⇒x2+y2+3x+y−11=0