Show that if `x^(2)+y^(2)=1`, then the point `(x,y,sqrt(1-x^(2)-y^(2)))` is at a distance 1 unit from the origin.

If the distance of the plane x - y + z + lambda = 0 from the point (1, 1, 1) is d_1 and the distance of this point from the origin is d_2 and d_2d_2 = 5 then find the value of lambda .

Find the distance of the plane 2x-y-2z+1=0 from the origin.

Solve the inequation -|y|+x-sqrt((x^(2)+y^(2)-1))ge1

Find the point on the line (x+2)/(3)=(y+1)/(2)=(z-3)/(2) at a distance of 3sqrt(2) from the point (1, 2, 3) .

P_1, P_2 are points on either of the two lines y- sqrt(3) |x| =2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P_1, P_2 on the bisector of the angle between the given lines. Thinking Process : Here, equation y- sqrt(3) |x| =2 represents two different lines for x gt 0 and x lt 0 and they are bisector of Y -axis. P_1 and P_2 are points at a distance 5 unit from point of intersection. The y coordinate of the foot of perpendicular on Y-axis is 2+5 cos ( 30^(@) ) .

If x^(2)+y^(2)+z^(2)-2xyz=1 , then the value of (dx)/(sqrt(1-x^(2)))+(dy)/(sqrt(1-y^(2)))+(dz)/(sqrt(1-z^(2))) is equal to………..

An equation of a plane parallel to the plane x-2y+2z-5=0 and at a unit distance from the origin is

Find (dy)/(dx) in the following: y= sin^(-1) (2x sqrt(1-x^(2))), (1)/(sqrt2) lt x lt 1

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

If x=sint,y=sinKt then show that (1-x^(2))y_2-xy_(1)+K^(2)y=0 .