Question

Number of points outside the hyperbola x^2 /25 - y^2 / 36 = 1 from where two perpendicular tangents can be drawn to the hyperbola

Answer 1

$\infty$
The locus of points from which perpendicular tangents can be drawn to a curve is called the directrix of the curve. For a hyperbola the directrix is the straight line which means there are infinitely many such points for a hyperbola.

Answer 2

Answer:

The two perpendicular tangents drawn to the hyperbola will always meet the director circle.

$hyperbola \: is \: \frac{ {x}^{2} }{25} - \frac{ {y}^{2} }{36} = 1$

Director circle:: x²+y²=a²-b²=25-36

x²+y²= -11

radius² never can be negative.

so "0" points are outside the hyperbola x² /25 - y² / 36 = 1 from where two perpendicular tangents can be drawn to the hyperbola.