Find the coordinates of the point equidistant from the point A(5,3),B(

1.	Find the coordinates of the point equidistant from the point A(5,3),B(5,-5)and C(1,-5)
Answer» Let the required points be P(x, y), thenPA = PB = PC. The points A, B, C are (5,3), (5, -5) and (1, -5) respectively{tex} \\Rightarrow{/tex}\xa0PA2\xa0= PB2\xa0= PC2{tex}\\Rightarrow{/tex}\xa0PA2 = PB2 and PB2 = PC2PA2 = PB2{tex}\\Rightarrow{/tex}\xa0(5 - x)2\xa0+ (3 - y)2\xa0= (5 - x)2\xa0+ (-5 -y)225 + x2\xa0- 10x + 9 + y2 - 6y = 25 + x2\xa0\xa0- 10x + 25 + y2\xa0+ 10y-6y - 10y = 25 - 9\xa0{tex}\\Rightarrow{/tex}\xa0-16y = 16y = -1and PB2 = PC2{tex}\\Rightarrow{/tex}\xa0(5 - x)2\xa0+ (-5 - y)2\xa0= (1 - x) + (-5 - y)225 + x2 - 10x + 25 + y2 + 10y = 1 + x2 - 2x + 25 + y2 + 10y-10x + 2x = -24\xa0{tex}\\Rightarrow{/tex}\xa0-8x = -24{tex}x = \\frac { - 24 } { - 8 } = 3{/tex}Hence, the point P is (3, -1)

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