A point P moves such that the tangents `PT_1` and `PT_2` from it to the hyperbola `4x^2 - 9y^2 = 36` are mutually perpendicular. Find the locus of P.

The tangents drawn from the point P to the ellipse 5x^(2) + 4y^(2) =20 are mutually perpendi­cular then P =

The tangents drawn from the point P to the ellipse 5x^(2) + 4y^(2) =20 are mutually perpendi­cular then P =

Find the asymptotes of the hyperbola 4x^(2)-9y^(2)=36

For the hyperbola 4x^2-9y^2=36 , find the Foci.

Find the equations of the tangents to the hyperbola (x ^(2))/(a ^(2)) - (y ^(2))/( b ^(2)) = 1 are mutually perpendicular, show that the locus of P is the circle x ^(2) + y ^(2) =a ^(2) -b ^(2).

If tangents drawn from the point (a,2) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 are perpendicular, then the value of a^(2) is

If tangents drawn from the point (a ,2) to the hyperbola (x^2)/(16)-(y^2)/9=1 are perpendicular, then the value of a^2 is _____