हिंदी

Find the Equations of the Tangent and Normal to the Parabola Y2 = 4ax at the Point (At2, 2at). - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equations of the tangent and normal to the parabola y2 = 4ax at the point (at2, 2at).

Advertisements

उत्तर

The equation of the given parabola is y2 = 4ax.

On differentiating y2 = 4ax with respect to x, we have:

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.3 [पृष्ठ २१३]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.3 | Q 22 | पृष्ठ २१३

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.


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 = x3 − 3x + 2 at the point whose x-coordinate is 3.


Find the equation of all lines having slope −1 that are tangents to the curve  `y = 1/(x -1), x != 1`


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

y = x3 at (1, 1)


Find the equation of the tangent to the curve `y = sqrt(3x-2)`  which is parallel to the line 4x − 2y + 5 = 0.

 

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 y2 = 2x3 at which the slope of the tangent is 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 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  \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?


Find the equation of the tangent and the normal to the following curve at the indicated points:

x = 3cosθ − cos3θ, y = 3sinθ − sin3θ? 


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


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?


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 ?


Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?


Find the angle of intersection of the following curve x2 + y2 = 2x and y2 = x ?


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


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


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


Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { and } xy = c^2\] ?


Find the slope of the normal at the point 't' on the curve \[x = \frac{1}{t}, y = t\] ?


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 ?


If the curve ay + x2 = 7 and x3 = y cut orthogonally at (1, 1), then a is equal to _____________ .


The slope of the tangent to the curve x = 3t2 + 1, y = t3 −1 at x = 1 is ___________ .


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 __________ .


Find the equation of tangents to the curve y = cos(+ y), –2π ≤ x ≤ 2π that are parallel to the line + 2y = 0.


Find the equation of a tangent and the normal to the curve `"y" = (("x" - 7))/(("x"-2)("x"-3)` at the point where it cuts the x-axis


Find the angle of intersection of the curves y2 = x and x2 = y.


Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.


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


Show that the line `x/"a" + y/"b"` = 1, touches the curve y = b · e– x/a at the point where the curve intersects the axis of y


The distance between the point (1, 1) and the tangent to the curve y = e2x + x2 drawn at the point x = 0


The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is


If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining `(0, 3/2)` and `(1/2, 2)`, then ______.


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


If β is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points `(3cosθ, sqrt(3) sinθ)` and `(-3sinθ, sqrt(3) cos θ); θ ∈(0, π/2)`; then `(2 cot β)/(sin 2θ)` is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×