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 :

Let a tangent to the curve $$\mathrm{y^2=24x}$$ meet the curve $$xy = 2$$ at the points A and B. Then the mid points of such line segments AB lie on a parabola with the

Let a line L pass through the point of intersection of the lines $$b x+10 y-8=0$$ and $$2 x-3 y=0, \mathrm{~b} \in \mathbf{R}-\left\{\frac{4}{3}\right\}$$. If the line $$\mathrm{L}$$ also passes through the point $$(1,1)$$ and touches the circle $$17\left(x^{2}+y^{2}\right)=16$$, then the eccentricity of the ellipse $$\frac{x^{2}}{5}+\frac{y^{2}}{\mathrm{~b}^{2}}=1$$ is :