Direct tangents are : (A) `y=sqrt3x+sqrt3,y=-sqrt3x+sqrt3`

Prove that the disgonals of the parallelogram whose sides are sqrt3x+y=0 , sqrt3y+x=0 ,'sqrt3x+y=1'and sqrt3y+x=1 are perpendicular to each other.

The equations of lines passing through the point (1,0) and at distance of (sqrt(3))/(2) units from the origin are (i) sqrt(3)x+y-sqrt(3)=0,sqrt(3)x-ysqrt(3)=0 (ii) sqrt(3)x+y+sqrt(3)=0,sqrt(3)x-y+sqrt(3)=0 (iii) x+sqrt(3)y-sqrt(3)=0,x-sqrt(3)y-sqrt(3)=0 (iv) none of these

sqrt(2)x+sqrt(3)y=0sqrt(3)x-sqrt(8)y=0

Solve the following equations : sqrt3x+sqrt2y = sqrt3 sqrt5x+ sqrt3y = sqrt3

sqrt(2)x+sqrt(3)y=0 sqrt(3)x+sqrt(8)y=0

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/(2) from the origin is sqrt(3)+y-sqrt(3)=0x+sqrt(3)y-sqrt(3)=0sqrt(3)x-y-sqrt(3)=0x-sqrt(3)y-sqrt(3)=0

The equation of two altitudes of an equilateral triangle are sqrt3x - y + 8 - 4 sqrt3 = 0 and sqrt3x + y - 12 - 4 sqrt3 = 0 . The equation of the third altitude is

The equation of the tangents to the ellipse 4x^2 + 3y^2 = 5 , which are inclined at 60^0 to the X-axis are : (A) y = x/sqrt(3) +- sqrt(65/12) (B) y = sqrt(3) +- sqrt(65/12) (C) y = sqrt(3)x +- sqrt(12/65) (D) none of these

sqrt (2x) -sqrt (3y) = 0sqrt (3x) -sqrt (3y) = 0