JEE MainMathematicsToughConic Sections

If a variable line has intercepts of e_1 and e_2on the
co-ordinate axes, where $\frac{e_{1}}{2}\&\frac{e_{2}}{2}$ are the
eccentricities of a hyperbola and its conjugate, then the line always
touches a fixed circle x^2 + y^2 = r^2, where is
o ml mRdsUærk,sa
x^2 + y^2 = r^2 djrh

Show answer and solution

Line is js[kk

xe_{2} + ye_{1} - e_{1}e_{2} = 0

.........(i)
Also rFkk

4\left( e_{1}^{2} + e_{2}^{2} \right) = e_{1}^{2}e_{2}^{2}

.........(ii)
It is tangent to circle if;g o`Ùk

Source: Grass-G / M-27 Mathematics Paper 2 15 Jan.docx

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