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AP EAMCET · Maths · Circle

If the tangent to the circle \(x^2+y^2-4 x+2 y-5=0\) at \((3,-4)\) cuts the circle \(x^2+y^2+16 x+2 y+10=0\) at \(A\) and \(B\), then the mid point of \(A B\) is:

  1. A \((-6,-9)\)
  2. B \((-9,-6)\)
  3. C \((-6,-7)\)
  4. D \((-7,-6)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((-6,-7)\)

Step-by-step Solution

Detailed explanation

Tangent to \(x^2+y^2-4x+2y-5=0\) at \((3,-4)\): \(x(3)+y(-4)-2(x+3)+1(y-4)-5=0\) \(3x-4y-2x-6+y-4-5=0\) \(x-3y-15=0\) Center of \(x^2+y^2+16x+2y+10=0\) is \(C(-8,-1)\). Midpoint of chord \(AB\) is foot of perpendicular from \(C(-8,-1)\) to \(x-3y-15=0\). Slope of chord \(AB\) is…
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