Question

A point $P$ moves such that the tangents $P{T}_1$ and $P{T}_2$ from it to the hyperbola $4x^2-9y^2=36$ are mutually perpendicular. Find the locus of $P$.

Answer 1

$\frac{x^2}{9}-\frac{y^2}{4}=1$,

Also, pt p locus represents the director circle of Hyperbola

$\therefore$ Dir circle for H$=x^2+y^2=a^2-b^2(a>b)$

$x^2+y^2=9-4$

$x^2+y^2=5$

$C(0,0),r=\sqrt{5}$.