Question

Given , what is the equation of the line that passes through the points (–p, –q) and (p, q)

Answer 1

Solution :
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Equation of a line passing through

the points ( x1, y1 ) and ( x2 , y2 ) is

y - y1 = [(y2-y1)/(x2-x1)]( x - x1 )
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Here ,

(x1 , y1 ) = ( -p , -q ) ,

( x2 , y2 ) = ( p , q )

Now , required equation is

y - (-q) = [(q+q)/(p+p)] ( x + p )

=> y + q = ( 2q/2p ) ( x + p )

=> y + q = ( q/p ) ( x + p )

=> p( y + q ) = q( x + p )

=> py + pq = qx + pq

=> qx - py = 0

Therefore,

Required equation is ,

qx - py = 0

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