English

If the tangent at (1, 1) on y2 = x(2 − x)2 meets the curve again at P, then P is - Mathematics and Statistics

Advertisements
Advertisements

Question

If the tangent at (1, 1) on y2 = x(2 − x)2 meets the curve again at P, then P is

Options

  • (4, 4)

  • (−1, 2)

  • (3, 6)

  • `(9/4, 3/8)`

MCQ

Solution

`(9/4, 3/8)`

shaalaa.com
Applications of Derivatives in Geometry
  Is there an error in this question or solution?
Chapter 2.2: Applications of Derivatives - MCQ

RELATED QUESTIONS

Find the equation of tangent and normal to the curve at the point on it.

y = x2 + 2ex + 2 at (0, 4)


Find the equations of tangents and normals to the following curves at the indicated points on them : x3 + y3 – 9xy = 0 at (2, 4)


Find the equations of tangents and normals to the following curves at the indicated points on them: `x^2 - sqrt(3)xy + 2y^2 = 5  "at"  (sqrt(3),2)`


Find the equations of tangents and normals to the following curves at the indicated points on them : 2xy + π sin y = `2pi  "at" (1, pi/2)`


Find the equations of tangents and normals to the following curves at the indicated points on them : x sin 2y = y cos 2x at `(pi/4, pi/2)`


Find the equations of tangents and normals to the following curve at the indicated points on them:

x = sin θ and y = cos 2θ at θ = `pi/(6)`


Find the equations of tangents and normals to the following curves at the indicated points on them : `x = sqrt(t), y = t  - (1)/sqrt(t)` at = 4.


Find the points on the curve y = x3 – 2x2 – x where the tangents are parllel to 3x – y + 1 = 0.


Find the equation of the tangents to the curve x2 + y2 – 2x – 4y + 1 =0 which a parallel to the X-axis.


A particle moves along the curve 6y = x3 + 2. Find the points on the curve at which y-coordinate is changing 8 times as fast as the x-coordinate.


If each side of an equilateral triangle increases at the rate of `(sqrt(2)"cm")/sec`, find the rate of increase of its area when its side of length 3 cm.


If water is poured into an inverted hollow cone whose semi-vertical angle is 30°, so that its depth (measured along the axis) increases at the rate of`( 1"cm")/sec`. Find the rate at which the volume of water increasing when the depth is 2 cm.


Choose the correct option from the given alternatives:

Let f(x) and g(x) be differentiable for 0 ≤ x ≤ 1 such that f(0) = 0, g(0), f(1) = 6. Let there exist a real number c in (0, 1) such that f'(c) = 2g'(c), then the value of g(1) must be ______.


Choose the correct option from the given alternatives :

If x = –1 and x = 2 are the extreme points of y = αlogx + βx2 + x`, then ______.


Choose the correct option from the given alternatives :

The normal to the curve x2 + 2xy – 3y2 = 0 at (1, 1)


Choose the correct option from the given alternatives :

The equation of the tangent to the curve y = `1 - e^(x/2)` at the point of intersection with Y-axis is


Choose the correct option from the given alternatives :

If the tangent at (1, 1) on y2 = x(2 – x)2 meets the curve again at P, then P is


Solve the following : If the curves ax2 + by2 = 1 and a'x2 + b'y2 = 1, intersect orthogonally, then prove that `(1)/a - (1)/b = (1)/a' - (1)/b'`.


Solve the following : Determine the area of the triangle formed by the tangent to the graph of the function y = 3 – x2 drawn at the point (1, 2) and the coordinate axes.


Solve the following : Find the equation of the tangent and normal drawn to the curve y4 – 4x4 – 6xy = 0 at the point M (1, 2).


The slope of the tangent to the curve x = 2 sin3θ, y = 3 cos3θ at θ = `pi/4` is ______.


If the line y = 4x – 5 touches the curve y2 = ax3 + b at the point (2, 3) then a + b is


Find the slope of normal to the curve 3x2 − y2 = 8 at the point (2, 2)


Find the slope of tangent to the curve x = sin θ and y = cos 2θ at θ = `pi/6`


Find the equation of normal to the curve y = 2x3 – x2 + 2 at `(1/2, 2)` 


Find points on the curve given by y = x3 − 6x2 + x + 3, where the tangents are parallel to the line y = x + 5.


Find the equation of tangent to the curve y = 2x3 – x2 + 2 at `(1/2, 2)`.


Find the equation of the tangents to the curve x2 + y2 – 2x – 4y + 1 = 0 which is parallel to the X-axis.


Find the points on the curve y = x3 – 9x2 + 15x + 3 at which the tangents are parallel to y-axis.


If the line 2x – y + 7 = 0 touches the curve y = ax2 + bx + 5 at (1, 9) then the values of ‘a’ and ‘b’ are ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×