Let a hyperbola passes through the focus of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$. The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse, also the produced of eccentricities of given ellipse and hyperbola is $$1$$, then

The equations of the common tangents to the parabola $$y = {x^2}$$ and $$y = - {\left( {x - 2} \right)^2}$$ is/are

Match the following : $$(3, 0)$$ is the pt. from which three normals are drawn to the parabola $${y^2} = 4x$$ which meet the parabola in the points $$P, Q $$ and $$R$$. Then

Column $${\rm I}$$
(A) Area of $$\Delta PQR$$
(B) Radius of circumcircle of $$\Delta PQR$$
(C) Centroid of $$\Delta PQR$$
(D) Circumcentre of $$\Delta PQR$$

Column $${\rm I}$$$${\rm I}$$
(p) $$2$$
(q) $$5/2$$
(r) $$(5/2, 0)$$
(s) $$(2/3, 0)$$

One angle of an isosceles $$\Delta $$ is $${120^ \circ }$$ and radius of its incircle $$ = \sqrt 3 $$. Then the area of the triangle in sq. units is