If `5-sqrt(3)=x+y sqrt(3)` then (x,y) is

If sqrt(x+y) +sqrt(y-x)=5, then (d^(2)y)/(dx ^(2))=

If x=8sqrt(3) and 3x=sqrt(3y) , what is the value of y?

The equation of the line which cuts of intercept 4 on x-ais and makes an angle of 60^(@) with the positive direction of the x-axis is (i) y=sqrt(3)(x+4) (ii) y=-sqrt(3)(x-4) (iii) y=sqrt(3)(x-4) (iv) y=-sqrt(3)(x+4)

The joint equation of two altitudes of an equilateral triangle is (sqrt(3)x-y+8-4sqrt(3)) (-sqrt(3)x-y+12 +4sqrt(3)) = 0 The third altitude has the equation

The equation of the circumcircle of the triangle formed by the lines y + sqrt(3)x = 6, y - sqrt(3) x = 6 and y = 0 , is-

If (sqrt(3)-1)/(sqrt(3)+1)=x+ysqrt(3) , find the value of x\ a n d\ y

If x=(sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3)) and y=(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3)) , then x+y+x y= (a) 9 (b) 5 (c) 17 (d) 7

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (A) sqrt(3)x^2 + sqrt(3)y^2 - 4x +4 sqrt(3)y = 0 (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

The distance of the point (1, 2, 3) from the plane x+y-z=5 measured along the straight line x=y=z is 5sqrt(3) (2) 10sqrt(3) (3) 3sqrt(10) 3sqrt(5) (5) 2sqrt(5)