If the tangent at a point P on the parabola $$y^2=3x$$ is parallel to the line $$x+2y=1$$ and the tangents at the points Q and R on the ellipse $$\frac{x^2}{4}+\frac{y^2}{1}=1$$ are perpendicular to the line $$x-y=2$$, then the area of the triangle PQR is :

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabola $$y^2=6x$$. The locus of its circumcentre is :

The distance of the point $$(6,-2\sqrt2)$$ from the common tangent $$\mathrm{y=mx+c,m > 0}$$, of the curves $$x=2y^2$$ and $$x=1+y^2$$ is :

The equations of the sides AB and AC of a triangle ABC are $$(\lambda+1)x+\lambda y=4$$ and $$\lambda x+(1-\lambda)y+\lambda=0$$ respectively. Its vertex A is on the y-axis and its orthocentre is (1, 2). The length of the tangent from the point C to the part of the parabola $$y^2=6x$$ in the first quadrant is :