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The distance of a point (x1 ,y1 ) from each of the two lines which pass through the origin of coordinates is z prove that the two lines are given by (x1y-y1x) whole square =z square (xsquare+ysquare)

The distance of a point (x1 ,y1 ) from each of the two lines which pass through the origin of coordinates is z prove that the two lines are given by (x1y-y1x) whole square =z square (xsquare+ysquare)
 

Grade:12th pass

1 Answers

Susmita
425 Points
3 years ago
As the line passes through the origin,so equation of the line can be written as
y=mx•••••(1)
Or,mx-y=0
The distance d(=z) from the point (x1,y1) to this straight line is
z=|mx1-y1|/root(m2+1)
Taking whole square on both side
z2(m2+1)=(mx1-y1)2 ••••••(2)
From equation(1)
y=mx
Or,m=y/x
Putting this value of m in eq(2)
z2{(y2+x2)/x2}=(yx1-xy1)2/x2
or,z2(x2+y2)=(yx1-xy1)2
please approve the answer if helped.
 

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