Find the shortest distance of the point (0, c) from the parabola y =` x^(2)` , where `(1)/(2) lt= c lt= 5 ` .

Find the distance of the point (3,-2,1) from the plane 2x -y+2z +3=0

Find the distance of the point (-6,0,0) from the plane 2x-3y+6z = 2 .

Find the distance of the point (-6, 0, 0) from the plane 2x - 3y + 6z = 2.

Find the distance of the point (3,-2,1) from the plane 2x-y+2z+3=0.

Find the distance of the point (-1, 1) from the line 12 (x + 6) = 5 (y - 2) .

Find the position of the point (-2,2) with respect to the parabola y^2-4y+9x+13=0 .

The shortest distance from the point (2,-7) to the circle x^(2)+y^(2)-14x-10y-151=0 is equal to .

If the distance of the point P (1,-2, 1) from the plane x + 2y - 2z = alpha where alpha > 0, is 5, then the foot of the perpendicular from P to the plane is :