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AP EAMCET · Maths · Circle

If the point \((1,4)\) lies inside the circle \(x^2+y^2-6 x-10 y+p=0\) and the circle does not touch or intersect the coordinates axes, then

  1. A \(0 < p < 34\)
  2. B \(25 < p < 29\)
  3. C \(9 < p < 25\)
  4. D \(7 < p < 29\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(25 < p < 29\)

Step-by-step Solution

Detailed explanation

Equation of given circle \(\begin{array}{rlrl} & x^2+y^2-6 x-10 y+p & =0 \\ \Rightarrow & (x-3)^2+(y-5)^2 & =34-p \\ \therefore & 34-p > 0 \Rightarrow p 25 \quad \ldots (ii) \\ \text {and } \sqrt{34-P} 9 \quad \ldots (iii) \end{array}\) \(\because\) Point \((1,4)\) lies inside…