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AP EAMCET · Maths · Circle

Let \(\alpha\) be an integer multiple of 8 . If 5 is the set or an possible values of \(\alpha\) such that the line \(6 x+8 y+\alpha=0\) intersects the circle \(x^2+y^2-4 x-6 y+9=0\) at two distinct points, then the number of elements in S is

  1. A \(4\)
  2. B \(6\)
  3. C \(2\)
  4. D \(1\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(4\)

Step-by-step Solution

Detailed explanation

\(x^2+y^2-4 x-6 y+9=0\) Radius \(=\sqrt{4+9-9}=2 ;\) Centre \(=(2,3)\) The line \(6 x+8 y+\alpha=0\) intersects the circle at two distinct points \(\therefore\) Length of Perpendicular from centre \( \lt \) radius…