` lf P(1+ 1/sqrt2 , 2+ 1/sqrt2) `be any point on a line, then the range of values of t for which the point P lies between the parallel lines x+ 2y= 1 and 2x+ 4y=15 is:

If P(1+t/(sqrt(2)),2+t/sqrt(2)) is any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1a n d2x+4y=15. is (a) (4sqrt(2))/3lttlt5(sqrt(2)) 6 (b) 0lttlt(5sqrt(2)) (c) 4sqrt(2)lttlt0 (d) none of these

If the point P(a^(2),a) lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x, then find the values of a.

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

A point at a distance of sqrt(6) from the origin which lies on the straight line (x-1)/1 = (y-2)/2=(z+1)/3 will be

From any point on the line (t+2)(x+y) =1, t ne -2 , tangents are drawn to the ellipse 4x^(2)+16y^(2) = 1 . It is given that chord of contact passes through a fixed point. Then the number of integral values of 't' for which the fixed point always lies inside the ellipse is

The total number of points on the curve x^2-4y^2=1 at which the tangents to the curve are parallel to the line x=2y is