Multiple choice

If there are two chords of the circle $ x ^ { 2 } + y ^ { 2 } - 2 x - 4 y - 20 = 0 $ which passes through ( h , k ) and bisected by x-axis then ____________.

  1. $

    ( h - 1 ) ^ { 2 } > 8 k

    $
  2. $

    \mathrm { h } ^ { 2 } > 8 \mathrm { k }

    $
  3. $

    ( h + 1 ) ^ { 2 } > 8 k

    $
  4. $

    k ^ { 2 } > 8 h

    $
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A Correct answer
Explanation

A chord passing through (h, k) and bisected by the x-axis means the midpoint is (x, 0). The chord equation is derived from the circle equation. The condition for the chord to exist and be bisected leads to the inequality (h-1)^2 > 8k.

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