English

The Slope of the Tangent to the Curve X = T2 + 3t – 8, Y = 2t2 – 2t – 5 at the Point (2,– 1) is - Mathematics

Advertisements
Advertisements

Question

The slope of the tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2,– 1) is

(A) `22/7`

(B) `6/7`

(C) `7/6`

(D) `(-6)/7`

Advertisements

Solution

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.6 [Page 243]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.6 | Q 20 | Page 243

RELATED QUESTIONS

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


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

y = x4 − 6x3 + 13x2 − 10x + 5 at (0, 5)


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 normal at the point (am2am3) for the curve ay2 = x3.


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.]


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

 

Find the equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1), where x1 = 2 and y1 > 0.


Find the slope of the tangent and the normal to the following curve at the indicted point  y = (sin 2x + cot x + 2)2 at x = π/2 ?


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


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 \[x = \frac{2 a t^2}{1 + t^2}, y = \frac{2 a t^3}{1 + t^2}\text { at } t = \frac{1}{2}\] ?


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 = asect, y = btant at t ?


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


Find the equation of the tangent to the curve  \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?


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


Show that the curves \[\frac{x^2}{a^2 + \lambda_1} + \frac{y^2}{b^2 + \lambda_1} = 1 \text { and } \frac{x^2}{a^2 + \lambda_2} + \frac{y^2}{b^2 + \lambda_2} = 1\] intersect at right angles ?


Find the point on the curve y = x2 − 2x + 3, where the tangent is parallel to x-axis ?


Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?


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


Write the equation of the normal to the curve y = x + sin x cos x at \[x = \frac{\pi}{2}\] ?


Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?


Write the slope of the normal to the curve \[y = \frac{1}{x}\]  at the point \[\left( 3, \frac{1}{3} \right)\] ?


Write the coordinates of the point at which the tangent to the curve y = 2x2 − x + 1 is parallel to the line y = 3x + 9 ?


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


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


The slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at the point (2, −1) is _____________ .


The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .


Show that the equation of normal at any point on the curve x = 3cos θ – cos3θ, y = 3sinθ – sin3θ is 4 (y cos3θ – x sin3θ) = 3 sin 4θ


The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.


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


The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.


Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to


If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×