Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$B$$.

The coordinates of $$A$$ and $$B$$ are

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$B$$.

The equation of the locus of the point whose distances from the point $$P$$ and the line $$AB$$ are equal, is

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$B$$.

The orthocentre of the triangle $$PAB$$ is

Consider a triangle $$ABC$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposit to vertices $$A, B$$ and $$C$$ respectively. Suppose $$a = 6,b = 10$$ and the area of the triangle is $$15\sqrt 3 $$, if $$\angle ACB$$ is obtuse and if $$r$$ denotes the radius of the incircle of the triangle, then r² is equal to :