Question

The circle x² + y² – 6x – 10y + p = 0 does not touch nor intersect the coordinate axes if the point (1, 4) lies inside the circle then –

• A. 0 < p < 29
• B. 25 < p < 29
• C. 25 < p < 35
• D. None of these

Answer 1

Answer: (B)

25 < p < 29

Answer 2

S = x² + y² – 6x – 10y + p = 0

P(1, 4)

g² – c < 0 ̃ 9 – p < 0 ̃ p – 9 > 0 ...(i)

f² – c < 0 ̃ 25 – p < 0 ̃ p – 25 > 0 ...(ii)

S₁ < 0

1 + 16 – 6 – 40 + p < 0 ̃ p – 29 < 0

p < 29 ...(iii)

comparing (i), (ii) & (iii)

25 < p < 29