Question

प्रश्न 5 Y- अक्ष पर स्थित किसी बिंदु के निर्देशांक ज्ञात कीजिए जो बिंदुओं (5.-2) व (3.4) से समदूरस्थ हैं।​

Answer 1

Question :

Find the coordinates of a point on the Y-axis which are equidistant from the points (5.-2) and (3.4).

$\underline{\textsf{Given:}}$

$\textsf{Points\;are\;(5,-2)\;and\;(3,4)}$

$\underline{\textsf{To find:}}$

$\textsf{The point on y axis which is equidistant from}$

$\textsf{the given two points}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the given points be A(5,-2) and B(3,4)}$

$\textsf{Let the required point on y axis be P(0,k)}$

$\textsf{As per given data,}$

$\mathsf{PA=PB}$

$\mathsf{\sqrt{(0-5)^2+(k+2)^2}=\sqrt{(0-3)^2+(k-4)^2}}$

$\mathsf{\sqrt{25+(k+2)^2}=\sqrt{9+(k-4)^2}}$

$\mathsf{Squaring\;on\;bothsides\;we\;get}$

$\mathsf{25+k^2+4+4k=9+k^2+16-8k}$

$\mathsf{4k+29=-8k+25}$

$\mathsf{4k+8k=-29+25}$

$\mathsf{12k=-4}$

$\mathsf{h=\dfrac{-4}{12}}$

$\implies\mathsf{k=\dfrac{-1}{3}}$

$\underline{\textsf{Answer:}}$

$\mathsf{The\;required\;point\;on\;x\;axis\;is \;(0,\frac{-1}{3})}$

$\underline{\textsf{Find more:}}$

Find the point on y-axis which is equidistant from the points (5,- 2) and (- 3,2)

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The point on the x-axis which is equidistant from the points (6, -2) and (5, 4) is ​

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