The point(s) on the curve y^3+\ 3x^2=...

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)`

`(pm4/(sqrt3),-2)`

`(pmsqrt(11/3),1)`

`(0,0)`

`(pm4/(sqrt3),2)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TANGENTS AND NORMALS
ML KHANNA|Exercise PROBLEM SET (1) (TRUE AND FALSE)|6 Videos
TANGENTS AND NORMALS
ML KHANNA|Exercise PROBLEM SET (1) (FILL IN THE BLANKS)|3 Videos
SELF ASSESSMENT TEST
ML KHANNA|Exercise OBJECTIVE MATHEMATICS |16 Videos
THE CIRCLE
ML KHANNA|Exercise Self Assessment Test (Fill in the blanks) |7 Videos

Similar Questions

Explore conceptually related problems

The point(s) on the curve y^(3)+3x^(2)=12y 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

ML KHANNA-TANGENTS AND NORMALS-SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)

The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is v...
Text Solution
|
For the curve x = t^2 - 1, y = t^2 - t, the tangent line is perpendicu...
Text Solution
|
The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2) -2t -5 at...
Text Solution
|
The tangent of the curve y = 2x^2 - x + 1 is parallel to the line y = ...
Text Solution
|
The tangentto the curve x^2 + y^2 - 2x- 3 = 0 is parallel to x-axis at...
Text Solution
|
Let C be the curve y^(3) - 3xy + 2 =0. If H is the set of points on th...
Text Solution
|
The curve x^3 -3xy^2 +2=0 and 3x^2y-y^3-2=0 cut at an angle of
Text Solution
|
The angle of intersection of the curve y = x^2 and 6y=7-x^2 at (1,1) i...
Text Solution
|
The equation of the tangent at the point P(t) ,wheret is any parameter...
Text Solution
|
The normal drawn at a point (at1^2,2at1)1 ) on the parabola y^2=4ax me...
Text Solution
|
The tangent to a given curve is perpendicular to x-axis if
Text Solution
|
The normal to a given curve is parallel to x-axis if
Text Solution
|
The point on the curve y^2 = x, the tangent at which makes an angle of...
Text Solution
|
The tangent to the curve y = e^(2x) at the point (0, 1) meets the x a...
Text Solution
|
The length of the subnormal to the parabola y^(2)=4ax at any point is ...
Text Solution
|
The normal at the.point (1, 1) on the curve 2y = 3 - x^2 is
Text Solution
|
The normal to the curve x=a(cos theta + theta sin theta), y=a(sin thet...
Text Solution
|
If the parametric equation of a curve is given by x=e^tcost,y=e^tsint,...
Text Solution
|
The angle of intersection of the curves y=x^(2), 6y=7-x^(3) at (1, 1),...
Text Solution
|
The equation of the tangent to the curve y=x+4/(x^2), that is parallel...
Text Solution
|