Findn k, if the line `y = sqrt(3) x + k` touches the circle `x^2 + y^2 = 16`.

The area of the circle x^2 + y^2 = 16 is :

If the straight line ax + by = 2 ; a, b!=0 , touches the circle x^2 +y^2-2x = 3 and is normal to the circle x^2 + y^2-4y = 6 , then the values of 'a' and 'b' are ?

The line 4y - 3x + lambda =0 touches the circle x^2 + y^2 - 4x - 8y - 5 = 0 then lambda=

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

If the values of m for which the line y=mx+2sqrt(5) touches the hyperbola 16x^(2)-9y^(2)=144 are the roots of the equation x^(2)-(a+b)x-4=0 , then the value of a+b is

Using integration, find the area of the region bounded by the circle x^2 + y^2 = 16 and line y=x in the first quadrant.

Find the equation of a circle, which touches the line x+ y = 5 at the point (-2, 7) and cuts the circle x^2+ y^2+ 4x - 6y +9 =0 orthogonally.

Find the value of lambda for which the plane x+y+z=sqrt(3)lambda touches the sphere x^2+y^2+z^2-2x-2y-2z=6.

Find the area of the region in the first quadrant enclosed by x-axis, line x = (sqrt3)y and the circle x^2+y^2= 4 .