English

Find the Equations of All Lines Having Slope 0 Which Are Tangent to the Curve Y = `1/(X^2-2x + 3)` - Mathematics

Advertisements
Advertisements

Question

Find the equations of all lines having slope 0 which are tangent to the curve  y =   `1/(x^2-2x + 3)`

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.3 [Page 212]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.3 | Q 12 | Page 212

RELATED QUESTIONS

Find the equations of the tangent and normal to the curve `x^2/a^2−y^2/b^2=1` at the point `(sqrt2a,b)` .


Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.


Find the point on the curve y = x3 − 11x + 5 at which the tangent is y = x − 11.

 

Find the equations of the tangent and normal to the given curves at the indicated points:

x = cos ty = sin t at  t = `pi/4`


Find the equation of the normals to the curve y = x3 + 2+ 6 which are parallel to the line x + 14y + 4 = 0.


Find the points on the curve y = `4x^3 - 3x + 5` at which the equation of the tangent is parallel to the x-axis.


Find the slope of the tangent and the normal to the following curve at the indicted point  x2 + 3y + y2 = 5 at (1, 1)  ?


Find the values of a and b if the slope of the tangent to the curve xy + ax + by = 2 at (1, 1) is 2 ?


If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b ?


Find the points on the curve xy + 4 = 0 at which the tangents are inclined at an angle of 45° with the x-axis ?


Find the points on the curve 2a2y = x3 − 3ax2 where the tangent is parallel to x-axis ?


At what points on the curve y = x2 − 4x + 5 is the tangent perpendicular to the line 2y + x = 7?


Find the equation of the tangent and the normal to the following curve at the indicated point \[y^2 = \frac{x^3}{4 - x}at \left( 2, - 2 \right)\] ?


Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( x_0 , y_0 \right)\] ?


Find the equation of the tangent and the normal to the following curve at the indicated points x = θ + sinθ, y = 1 + cosθ at θ = \[\frac{\pi}{2}\] ?


Find the equation of the normal to the curve ay2 = x3 at the point (am2, am3) ?


Find the equation of the tangent to the curve x = sin 3ty = cos 2t at

\[t = \frac{\pi}{4}\] ?


Find the angle of intersection of the following curve y2 = x and x2 = y  ?


Find the angle of intersection of the following curve  y = x2 and x2 + y2 = 20  ?


Find the angle of intersection of the following curve y = 4 − x2 and y = x2 ?


Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x?


Write the angle made by the tangent to the curve x = et cos t, y = et sin t at \[t = \frac{\pi}{4}\] with the x-axis ?


Write the angle between the curves y = e−x and y = ex at their point of intersections ?


The point on the curve y2 = x where tangent makes 45° angle with x-axis is ____________________ .


The angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .


The line y = mx + 1 is a tangent to the curve y2 = 4x, if the value of m is ________________ .


Find the angle of intersection of the curves \[y^2 = 4ax \text { and } x^2 = 4by\] .

 

The equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.


If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is ______.


For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?


The point on the curves y = (x – 3)2 where the tangent is parallel to the chord joining (3, 0) and (4, 1) is ____________.


The tangent to the parabola x2 = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.


If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then


Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is:


Which of the following represent the slope of normal?


The Slope of the normal to the curve `y = 2x^2 + 3 sin x` at `x` = 0 is


The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.


If m be the slope of a tangent to the curve e2y = 1 + 4x2, then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×