True or False :
Normal form of the line `sqrt(3) x + y + 2 = 0` is `(sqrt(3))/2x + 1/(2)y = -1`

Find angles between the lines sqrt3 x+ y = 1 and x + sqrt3y = 1.

True or False statements : sin^-1 sqrt3 + cos^-1 sqrt3 = pi/2

Find the values of theta and p, if the equation x cos theta + y sin theta = p is the normal form of the line sqrt3 x+y + 2 = 0 .

Statement True/ False: br The slope of the normal to the curve y = 2x^2 + 3 sinx at x = 0 is -1/3

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation sqrt3 x+ y -6 = 0 and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. The equation of circle C A. y=(2)/(sqrt3)+x+1,y=-(2)/(sqrt3)x-1 B. y=(1)/(sqrt3)x,y=0 C. y=(sqrt3)/(2)x+1,y=-(sqrt3)/(2)x-1 D. y=sqrt3x,y=0

Slope of normal to the line 2x-3y+4=0 is ____________

Prove that the diagonals of the parallelogram formed by the four straight lines : sqrt3x+y=0, sqrt3y+x=0 , sqrt3x+y=1 and sqrt3y+x+1 are at right angle to one another.

Find the equations of the bisectors of the angles formed by the following pairs of lines : x+sqrt3 y =6+2 sqrt3 and x- sqrt3 y =6-2 sqrt3 .