Search any question & find its solution
Question:
Answered & Verified by Expert
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 $\mathrm{eq}^{\mathrm{n}}$ of this circle is
Options:
Solution:
2166 Upvotes
Verified Answer
The correct answer is:
$x^2+y^2=a^2-b^2$
Equation of hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
Any tangent to hyperbola are $y=m x \pm \sqrt{a^2 m^2-b^2}$
Also tangent perpendicular to this is $y=\frac{-1}{m} \times \pm \sqrt{\frac{a^2}{m^2}-b^2}$
Eliminating $m$, we get $x^2+y^2=a^2-b^2$.
Any tangent to hyperbola are $y=m x \pm \sqrt{a^2 m^2-b^2}$
Also tangent perpendicular to this is $y=\frac{-1}{m} \times \pm \sqrt{\frac{a^2}{m^2}-b^2}$
Eliminating $m$, we get $x^2+y^2=a^2-b^2$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.