AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

(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