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# For the variable t, the locus of the points of intersection of lines x–2y = t and x+2y=1/t is?

Vikas TU
14149 Points
one year ago

Let the equation of any line passing through the point of intersection of the given lines be

(x+2y-1)+a×(2x-y-1)=0

Reducing the equation to its intercept form…

(x×(1+2a)/(1+a))+(y×(2-a)/(1+a))=1

Therefore coordinates of A and B,where this line meets the coordinate axes respectively…

A=((1+a)/(1+2a),0) on x axis and,

B=(0,(1+a)/(2-a)) on y axis…

Mid point of AB=((1+a)/(2+4a),(1+a)/(4-2a)

Now we find the locus of this point by eliminating ‘a’ between the two expressions

x=(1+a)/(2+4a) &

y=(1+a)/(4-2a)

y=x/(10x-3)……..required locus …