Question

The point which lies on y-axis at a distance of 6 units from the point (0, 1)

Answer 1

$\large{\underline{\bf{\purple{Given:-}}}}$

• ✦ Distance between two points= 6unit's
• ✦ one cordinate is given =(0,1)

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• ✦we need to find another cordinate on y axis.

$\huge{\underline{\bf{\red{Solution:-}}}}$

Let the required points be PA p(x ,y)

Then,

PA = 6 unit's

• P(0,1) , A(x ,0)

$\mapsto \rm\:PA = \sqrt{(y_2-y_1)^{2} } \: \\ \\ \mapsto \rm\:6=\sqrt{(y-1)^2} \\ \\ \mapsto \rm\ 6=(y-1) \\ \\\mapsto \rm\ \: \: 6+1=y \\ \\ \mapsto \rm\:y=7$

Hence,

co - ordinates on y axis are p(7,0)

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Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Co-ordinates \ of \ point \ are \ (0,-5)}$

$\sf{or \ (0,7)}$

$\sf\orange{Given:}$

$\sf{\implies{The \ point \ lies \ on \ y-axis}}$

$\sf{\implies{The \ point \ is \ at \ distance \ of }}$

$\sf{6 \ units \ from \ the \ point \ (0,1)}$

$\sf\pink{To \ find:}$

$\sf{Co-ordinates \ of \ point.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ point \ with \ co-ordinates \ (0,1)}$

$\sf{be \ A \ and \ point \ at \ distance \ of}$

$\sf{6 \ units \ be \ B \ (x2,y2)}$

$\sf{Both \ points \ lie \ on \ y-axis }$

$\sf{Hence, \ their \ x-co-ordinate \ will \ be \ zero.}$

$\sf{Case(I)}$

$\sf{d(A,B)=\sqrt{(y1-y2)^{2}}}$

$\sf{6=\sqrt{(1-y2)^{2}}}$

$\sf{(1-y2)=6}$

$\sf{y2=1-6}$

$\sf{y2=-5}$

$\sf{Case(II)}$

$\sf{d(B,A)=\sqrt{(y2-1)^{2}}}$

$\sf{6=y2-1}$

$\sf{y2=6+1}$

$\sf{y2=7}$

$\sf\purple{\tt{\therefore{Co-ordinates \ of \ point \ are \ (0,-5) }}}$

$\sf\purple{\tt{or \ (0,7)}}$