The point(s) on the curve `y^3+\ 3x^2=12 y` where the tangent is vertical, is(are) ?? `(+-4/(sqrt(3)),\ -2)` (b) `(+-\ sqrt((11)/3,\ )\ 1)` `(0,\ 0)` (d) `(+-4/(sqrt(3)),\ 2)`

The number of point(s) on the curve y^(3)=12y-3x^(2) where a tangents is vertical is/are

The point (s) on the curve y^3+3x^2=12y . Where the tangent is parallel to Y- axis , is (are)

The points on the curve y=sqrt(x-3) , where the tangent is perpendicular to the line 6x+3y-5=0 are

Find a point on the curve y=(x-3)^2 , where the tangent is parallel to the line joining (4,\ 1) and (3,\ 0) .

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 (0,0)(b)(sqrt(3),-(sqrt(3))/(2))(-2,(2)/(3))(d)(-sqrt(3),(sqrt(3))/(2))

The shortest distance between line y-x=1 and curve is : (1)(sqrt(3))/(4) (2) (3sqrt(2))/(8) (3) (8)/(3sqrt(2))(4)(4)/(sqrt(3))

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

On the ellipse 2x^(2)+3y^(2)=1 the points at which the tangent is parallel to 4x=3y+4 are ( i )((2)/(sqrt(11)),(1)/(sqrt(11))) or (-(2)/(sqrt(11)),-(1)/(sqrt(11))) (ii) (-(2)/(sqrt(11)),(1)/(sqrt(11))) or ((2)/(sqrt(11)),-(1)/(sqrt(11))) (iii) (-(2)/(5),-(1)/(5)) (iv) ((3)/(5),(2)/(5)) or (-(3)/(5),-(2)/(5))

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