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AP EAMCET · Maths · Circle

If \(L_1\) represents the radical axis of circles \(x^2+y^2-4 x-6 y+5=0\) and \(x^2+y^2-2 x-4 y-1=0\) and \(L_2\) represents the radical axis of \(x^2+y^2+2 x+2 y-7=0\) and \(x^2+y^2+x+y+9=0\), then

  1. A \(L_1\) is parallel to \(L_2\).
  2. B \(L_1\) is perpendicular to \(L_2\).
  3. C \(L_1\) and \(L_2\) intersect at an angle \(30^{\circ}\).
  4. D \(L_1\) and \(L_2\) intersect at \((1,7)\).
Verified Solution

Answer & Solution

Correct Answer

(A) \(L_1\) is parallel to \(L_2\).

Step-by-step Solution

Detailed explanation

Circles \(\rightarrow x^2+y^2-4 x-6 y+5=0 \quad \ldots\left(S_1\right)\) and \(x^2+y^2-2 x-4 y-1=0\) Equation of radical axis is \[ \begin{aligned} & S_1-S_2=0 \\ & L_1:\left(x^2+y^2-4 x-6 y+5\right)- \\ & \quad\left(x^2+y^2-2 x-4 y-1\right)=0 \end{aligned} \]…