If a circle cuts a rectangular hyperbola xy = | vedclass

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Question

(b) Let equation of circle is ${x^2} + {y^2} = {a^2}$

Parametric form of $xy = {c^2}$ are $x = ct,\,\,\,y = \frac{c}{t}$

==> ${c^2}{t^2} + \f

Vedclass · Accepted Answer

${t_1}{t_2}{t_3}{t_4} = 1$

Vedclass · Answer

(b) Let equation of circle is ${x^2} + {y^2} = {a^2}$

Parametric form of $xy = {c^2}$ are $x = ct,\,\,\,y = \frac{c}{t}$

==> ${c^2}{t^2} + \frac{{{c^2}}}{{{t^2}}} = {a^2}$

==> ${c^2}{t^4} - {a^2}{t^2} + {c^2} = 0$

Product of roots will be, ${t_1}{t_2}{t_3}{t_4} = \frac{{{c^2}}}{{{c^2}}} = 1$.

If a circle cuts a rectangular hyperbola $xy = {c^2}$ in $A, B, C, D$ and the parameters of these four points be ${t_1},\;{t_2},\;{t_3}$ and ${t_4}$ respectively. Then

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