The point `(x , y)` lies on the line `2x+3y=6.` The smallest value of the quantity `sqrt(x^2+y^2)` is `mdot` then the value of `sqrt(13)` `m` is_______

If (x,y) lies on the ellipse x^(2)+2y^(3) = 2 , then maximum value of x^(2)+y^(2)+ sqrt(2)xy - 1 is

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

A rectangle with one side lying along the x-axis is to be inscribed in the closed region of the x y plane bounded by the lines y=0,y=3x ,a n dy=30-2xdot If M is the largest area of such a rectangle, then the value of (2M)/(27) is_______

If x , y in R satisfies (x+5)^2+(y-12)^2=(14)^2, then the minimum value of sqrt(x^2+y^2) is__________

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 adot

Find the smallest possible value of x^(2)+y^(2) given that x + y = 10.

If line 3x-a y-1=0 is parallel to the line (a+2)x-y+3=0 then find the value of adot

If y = 2sqrt2x+c is a tangent to the circle x^(2) +y^(2) = 16 , find the value of c.