Number of points from where perpendicular tangents can be drawn to the curve `x^2/16-y^2/25=1` is

There exist two points P and Q on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that PObotOQ , where O is the origin, then the number of points in the xy -plane from where pair of perpendicular tangents can be drawn to the hyperbola , is

Number of perpendicular tangents that can be drawn on the ellipse (x^(2))/(16)+(y^(2))/(25)=1 from point (6, 7) is

The points on the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 from where mutually perpendicular tangents can be drawn to circle x^(2) + y^(2) = a^(2)/2 is /are

If eight distinct points can be found on the curve |x|+|y|=1 such that from eachpoint two mutually perpendicular tangents can be drawn to the circle x^(2)+y^(2)=a^(2), then find the tange of a.

Number of points on hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/(b ^(2)) =1 from were mutually perpendicular tangents can be drawn to circel x ^(2) + y ^(2)=a ^(2) is