Find the points on y axis whose perpendicular distances from the line 4x-3y-12=0 is 3.

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Please find below the solution to the asked query:

As point lies on Y-axis, hence let the co-ordinates of point be 0,a.Perpendicular distance between points x1,y1 and line ax+by+c=0 is given by:p=ax1+by1+ca2+b2Hence distance between 0,a  and 4x-3y-12=0 will be given by:p=4×0-3×a-1242+-32-3a-1216+9=3  Given that p=3-3a+1225=33a+125=33a+12=153a+12=±153a+12=15 or 3a+12=-153a=15-12 or 3a=-15-123a=3 or 3a=-27a=1 or a=-9Hence co-ordinates of point will be 0,1 or 0,-9.

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