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The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}
Hi student,we have rectangular hyperbolaxy=c2take a general point on this in parametric P(ct, c/t)Now tangent at point P is T=0xy1 + yx1 = 2c2So in parametricx(c/t) + y(ct) = 2c2x/t + ty – 2c = 0….….…...(1)Now centre is O(0,0)LET foot of Perpendiculer be F(h,k)So OF tangentSo product of slopes = -1k/h * (-1/t2)= -1hence k/h= t2 ….…..(2)Also prependicular distance OF is Now Put t2=k/h in above you will get the answerI hope the solution is clear
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