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

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

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

Find x and y if: (3/sqrt(5) x-5)+i2 sqrt (5) y= sqrt(2)

The equation of the common tangent touching the circle (x-3)^2+y^2=9 and the parabola y^2=4x above the x-axis is sqrt(3)y=3x+1 (b) sqrt(3)y=-(x+3) (C) sqrt(3)y=x+3 (d) sqrt(3)y=-(3x-1)

Find the equation of the tangent line to the curve y=sqrt(5x-3)-2 which is parallel to the line 4x-2y+3=0

Find the equation of the tangent line to the curve y=sqrt(5x-3)-2 which is parallel to the line 4x-2y+3=0 .

The point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as (a) (6,-4sqrt(3)) (b) (6,4sqrt(3)) (c) (-6,-4sqrt(3)) (d) (-6,4sqrt(3))

3x + 4y = 12 sqrt2 is the tangent to the ellipse x^2/a^2 + y^2/9 = 1 then the distance between focii of ellipse is-

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

Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an angle of pi/4 to the x-axis are (a) (0,0) (b) (sqrt(3),-(sqrt(3))/2) (c) (-2,2/3) (d) (-sqrt(3),(sqrt(3))/2)