InterviewSolution
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InterviewSolution
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If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k. Also, find the length of AP. |
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Answer» Correct Answer - `(k =-3 rArr AP = sqrt(41)), (k = -1 rArr AP = 5)` `PA = PB rArr PA^(2) = PB^(2)` `rArr (2+2)^(2) + (2-k)^(2) = (2+2k)^(2) + (2+3)^(2)` `rArr (2-k)^(2) - (2 +2k)^(2) = 25-16 =9` `rArr (4+k^(2)-4k) -(4+4k^(2) +8k) = 9` `rArr 3k^(2) + 12k + 9=0` `rArr k^(2) + 4k +3 =0 rArr (k +3)(k+1) = 0` `rArr k = -3 "or" k =-1` Case 1. When k = -3, we have AP = distance between A(-2, -3) and P(2, 2) = `sqrt(41)` units. Case 2. When k =-1, we have AP = distance between A(-2, -1) and P(2, 2) = sqrt(25) = 5 units. |
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