मराठी

Find the Slope of the Normal to the Curve X = Acos3θ, Y = Asin3θ At `Theta = Pi/4` - Mathematics

Advertisements
Advertisements

प्रश्न

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

उत्तर

It is given that x = acos3θ and y = asin3θ.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Application of Derivatives - Exercise 6.3 [पृष्ठ २११]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 6 Application of Derivatives
Exercise 6.3 | Q 5 | पृष्ठ २११

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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.


The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and 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 = x4 − 6x3 + 13x2 − 10x + 5 at (1, 3)


Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = −2 are parallel.


Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.


Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]


The line y = x + 1 is a tangent to the curve y2 = 4x at the point

(A) (1, 2)

(B) (2, 1)

(C) (1, −2)

(D) (−1, 2)


Find the slope of the tangent and the normal to the following curve at the indicted point x = a (θ − sin θ), y = a(1 − cos θ) at θ = −π/2 ?


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\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text{ at }\left( a\cos\theta, b\sin\theta \right)\] ?


Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at \[\left( \frac{a}{m^2}, \frac{2a}{m} \right)\] ?


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


Find the equation of the tangent and the normal to the following curve at the indicated point  y2 = 4x at (1, 2)  ?


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 tangent and the normal to the following curve at the indicated points x = a(θ + sinθ), y = a(1 − cosθ) at θ ?


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


The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x − 5. Find the values of a and b ?


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


Find the equations of all lines having slope 2 and that are tangent to the curve \[y = \frac{1}{x - 3}, x \neq 3\] ?


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


Find the angle of intersection of the following curve  2y2 = x3 and y2 = 32x ?


Find the angle of intersection of the following curve  x2 = 27y and y2 = 8x ?


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


Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?


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


If the straight line xcos \[\alpha\] +y sin \[\alpha\] = p touches the curve  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\] then prove that a2cos2 \[\alpha\] \[-\] b2sin\[\alpha\] = p?


Write the equation of the normal to the curve y = cos x at (0, 1) ?


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


The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes is

(a) \[\left( 4, \frac{8}{3} \right)\]

(b) \[\left( - 4, \frac{8}{3} \right)\]

(c) \[\left( 4, - \frac{8}{3} \right)\]

(d) none of these

 


Find the equation of tangent to the curve `y = sqrt(3x -2)` which is parallel to the line 4x − 2y + 5 = 0. Also, write the equation of normal to the curve at the point of contact.


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


Find the equation of the normal lines to the curve 3x2 – y2 = 8 which are parallel to the line x + 3y = 4.


At what points on the curve x2 + y2 – 2x – 4y + 1 = 0, the tangents are parallel to the y-axis?


The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point ____________.


Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are ____________.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×