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

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) x +- sqrt(65/12) (C) y = sqrt(3)x +- sqrt(12/65) (D) none of these

sqrt(2)x + sqrt(3)y=0 sqrt(5)x - sqrt(2)y=0

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

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

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

The equations of the lines which pass through the point (3,-2) and are inclined at 60^(@) to the line sqrt(3)x+y=1 are (i) y+2=0,sqrt(3)x-y-2-3sqrt(3)=0 (ii) x-2=0,sqrt(3)x-y+2+3sqrt(3)=0 (iii) x-3=0,sqrt(3)x-y-2-3sqrt(3)=0 (iv) none of these

A vertex of an equilateral triangle is at (2, 3), and th equation of the opposite side is x+y=2 , then the equaiton of the other two sides are (A) y=(2+sqrt(3)) (x-2), y-3=2sqrt(3)(x-2) (B) y-3=(2+sqrt(3) (x-2), y-3= (2-sqrt(3) (x-2) (C) y+3=(2-sqrt(3)(x-2), y-3=(2-sqrt(3) (x+2) (D) none of these

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is: (a)y=4 sqrt(5) x +20 (b)y=4 sqrt(3) x -12 (c)y=0 (d) y=-4 sqrt(5) x -20

Direct tangents are : (A) y=sqrt(3)x+sqrt(3),y=-sqrt(3)x+sqrt(3)

If x=(2)/(sqrt(3)-sqrt(5)) and y=(2)/(sqrt(3)+sqrt(5)) , then x+y = _______ .