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निर्देशांक ज्यामिति

Question
CBSEHHIMAH10010039

x-अक्ष पर वह बिंदु ज्ञात कीजिए जो (2, -5) और (-2, 9) से समदूरस्थ हैं।

Solution

माना बिंदु P के निर्देशांक (x, 0) हैं।
माना बिंदु हैं A(2, -5) और B(—2, 9)
space space space space space space space AP space equals space BP
rightwards double arrow space space space space square root of left parenthesis 2 minus straight x right parenthesis squared plus left parenthesis negative 5 minus 0 right parenthesis squared end root
equals space space space space square root of left curly bracket straight x minus left parenthesis negative 2 right parenthesis right curly bracket squared plus left parenthesis 0 minus 9 right parenthesis squared end root
rightwards double arrow space space space space square root of left parenthesis 2 minus straight x right parenthesis squared plus left parenthesis negative 5 right parenthesis squared end root equals square root of open parentheses straight x minus 2 close parentheses squared plus left parenthesis negative 9 right parenthesis squared end root
rightwards double arrow space space space square root of left parenthesis 2 right parenthesis squared left parenthesis straight x right parenthesis squared minus 2 left parenthesis 2 right parenthesis left parenthesis straight x right parenthesis plus 25 end root
equals space space space square root of left parenthesis straight x right parenthesis squared plus left parenthesis 2 right parenthesis squared plus 2 left parenthesis straight x right parenthesis left parenthesis 2 right parenthesis plus 81 end root
rightwards double arrow space space space square root of 4 plus straight x squared minus 4 straight x plus 25 end root equals square root of straight x squared plus 4 plus 4 straight x plus 81 end root
rightwards double arrow space space space square root of straight x squared minus 4 straight x plus 29 end root equals square root of straight x squared plus 4 straight x plus 85 end root
x2 - 4x + 29 = x2 + 4x + 85
⇒    -4x - 4x = 85 - 29
⇒    -8x = 56⇒    x = -7
इसलिए, बिंदु होगा = (-7, 0)