The locus of the point of intersection of any | vedclass

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Question

(b) Equation of hyperbola is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

Any tangent to hyperbola are $y = mx \pm \sqrt {{a^2}{m^2} - {

Vedclass · Accepted Answer

${x^2} + {y^2} = {a^2} - {b^2}$

Vedclass · Answer

(b) Equation of hyperbola is $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$

Any tangent to hyperbola are $y = mx \pm \sqrt {{a^2}{m^2} - {b^2}} $

Also tangent perpendicular to this is $y = \frac{{ - 1}}{m}x \pm \sqrt {\frac{{{a^2}}}{{{m^2}}} - {b^2}} $

Eliminating $m$, we get ${x^2} + {y^2} = {a^2} - {b^2}$.

The locus of the point of intersection of any two perpendicular tangents to the hyperbola is a circle which is called the director circle of the hyperbola, then the eqn of this circle is

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