The minimum distance of a point on the curve y = x²−4 from the origin is :

If the tangent at a point P, with parameter t, on the curve x = 4t² + 3, y = 8t³−1, t $$ \in $$ R, meets the curve again at a point Q, then the coordinates of Q are :

A wire of length $$2$$ units is cut into two parts which are bent respectively to form a square of side $$=x$$ units and a circle of radius $$=r$$ units. If the sum of the areas of the square and the circle so formed is minimum, then:

Consider :
f $$\left( x \right) = {\tan ^{ - 1}}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right),x \in \left( {0,{\pi \over 2}} \right).$$

A normal to $$y = $$ f$$\left( x \right)$$ at $$x = {\pi \over 6}$$ also passes through the point: