(b) Equation of given circle x2+y2−6x−10y+p=0 ⇒(x−3)2+(y−5)2=34−p ∴34−p>0⇒p<34.....(i) ∵ Circle doesn't touch or intersect the coordinate axis, so √34−p<3, (for X-axis) ⇒34−p<9⇒p>25... (ii) and √34−P<5, (for Y-axis) ⇒34−p<25... (iii) ⇒p>9 ∵ Point (1,4) lies inside the circle, so ⇒1+16−6−40+p<0 p<29.....(iv) From inequalities Eqs. (i), (ii), (iii) and (iv), we get 25<p<29