English

Find the Equations of the Tangent and Normal to the Given Curves at the Indicated Points: Y = X2 At (0, 0) - Mathematics

Advertisements
Advertisements

Question

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

y = x2 at (0, 0)

Solution

The equation of the curve is y = x2.

On differentiating with respect to x, we get:

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 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.3 | Q 14.4 | Page 212

RELATED QUESTIONS

Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.


Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.


Find the slope of the normal to the curve x = acos3θy = asin3θ at `theta = pi/4`


Find points on the curve `x^2/9 + "y"^2/16 = 1` at which the tangent is parallel to x-axis.


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is perpendicular to the line 5y − 15x = 13.


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 equations of the tangent and normal to the hyperbola `x^2/a^2 - y^2/b^2` at the point `(x_0, y_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 \[y = \sqrt{x^3} \text { at } x = 4\] ?


Find the points on the curve y = x3 − 2x2 − 2x at which the tangent lines are parallel to the line y = 2x− 3 ?


Find the point on the curve y = x2 where the slope of the tangent is equal to the x-coordinate of the point ?


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


Find the points on the curve \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is  parallel to x-axis ?


 Find the equation of the tangent and the normal to the following curve at the indicated point y = x4 − 6x3 + 13x2 − 10x + 5 at x = 1? 


Find the equation of the tangent and the normal to the following curve at the indicated point  y = x2 at (0, 0) ?


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


Find the equation of the tangent and the normal to the following curve at the indicated point 4x2 + 9y2 = 36 at (3cosθ, 2sinθ) ?    


Find the equation of the tangent to the curve x = θ + sin θ, y = 1 + cos θ at θ = π/4 ?


Find the equation of the tangent and the normal to the following curve at the indicated points x = at2, y = 2at at t = 1 ?


Find the equation of the normal to the curve x2 + 2y2 − 4x − 6y + 8 = 0 at the point whose abscissa is 2 ?


At what points will be tangents to the curve y = 2x3 − 15x2 + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?


Show that the following curve intersect orthogonally at the indicated point x2 = 4y and 4y + x2 = 8 at (2, 1) ?


Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?


The angle between the curves y2 = x and x2 = y at (1, 1) is ______________ .


The equation of the normal to the curve x = a cos3 θ, y = a sin3 θ at the point θ = π/4 is __________ .


If the curves y = 2 ex and y = ae−x intersect orthogonally, then a = _____________ .


The point on the curve y = 6x − x2 at which the tangent to the curve is inclined at π/4 to the line x + y= 0 is __________ .


Any tangent to the curve y = 2x7 + 3x + 5 __________________ .


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

 

 Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).


Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.


Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.


Find the co-ordinates of the point on the curve `sqrt(x) + sqrt(y)` = 4 at which tangent is equally inclined to the axes


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


The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.


The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan `"t"/2`)} at the point ‘t’ is ____________.


Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).


Find the equation to the tangent at (0, 0) on the curve y = 4x2 – 2x3


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×