ExamBro
ExamBro
AP EAMCET · Maths · Circle

The circle \(x^2+y^2-8 x-12 y+\alpha=0\) lies in the first quadrant without touching the coordinate axes. If \((6,6)\) is an interior point to the circle, then

  1. A \(4 \lt \alpha \lt 6\)
  2. B \(6 \lt \alpha \lt 16\)
  3. C \(16 \lt \alpha \lt 48\)
  4. D \(36 \lt \alpha \lt 48\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(36 \lt \alpha \lt 48\)

Step-by-step Solution

Detailed explanation

\((6,6)\) is an interior point of \(x^2+y^2-8 x-12 y+\alpha=0\) \(\Rightarrow 36+36-48-72+\alpha \lt 0 \Rightarrow \alpha \lt 48\) Also, radius \( \lt x\) and \(y\) coordinate of centre \(\Rightarrow \sqrt{16+36-\alpha} \lt 4\) and 6 \(\Rightarrow 52-\alpha \lt 16\) and…