Question:
<p>A circle S = 0 passes through points of intersection of circles x<sup>2</sup> + y<sup>2</sup> - 2x + 4y = 1 and x<sup>2</sup> + y<sup>2</sup> + 4x - 2y - 5 = 0 and cuts the circle x<sup>2</sup> + y<sup>2</sup> - 4 = 0 orthogonally. Then the length of tangent from origin on circle S = 0, is :</p>
<p style="display:inline">0</p>
<p style="display:inline">3</p>
<p style="display:inline">2</p>
<p style="display:inline">1</p>
Step-by-Step Solution
Key Concept: A circle passing through the intersection of two circles can be expressed as S₁ + λL = 0 where L is the radical axis. Use the orthogonality condition 2g₁g₂ + 2f₁f₂ = c₁ + c₂ to find λ, then calculate the length of tangent as √(g² + f² - c).
<p>2</p>
Correct Answer: C