Question

y अक्ष पर वह बिंदु ज्ञात करें जो बिंदु A(6,5) or B ( -4,3) से समान दूरी पर हो​

Answer 1

Find the point on the Y axis that is equally spaced from the point A (6,5) or B (-4,3).

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

$\textsf{Points are A(6,5) and B(-4,3)}$

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

$\textsf{The point on y axis which is equally spaced from A and B}$

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

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

$\textsf{As per given data,}$

$\mathsf{AP=BP}$

$\mathsf{\sqrt{(0-6)^2+(y-5)^2}=\sqrt{(0+4)^2+(y-3)^2}}$

$\mathsf{\sqrt{36+(y-5)^2}=\sqrt{16+(y-3)^2}}$

$\textsf{squaring on bothsides, we get}$

$\mathsf{36+(y-5)^2=16+(y-3)^2}$

$\mathsf{(y-5)^2-(y-3)^2=16-36}$

$\mathsf{y^2+25-10y-y^2-9+6y=-20}$

$\mathsf{-4y+16=-20}$

$\mathsf{-4y=-20-16}$

$\mathsf{-4y=-36}$

$\mathsf{y=9}$

$\therefore\textsf{The required point on y axis is (0,9)}$

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