Application of Derivatives Lecture 8

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सफलता एक चुनौती है इसे स्वीकार करो
क्या कमी रह गई देखो और सुधार करो
कुछ किए बिना ही जय जयकार नहीं होती
कोशिश करने वालों की कभी हार नहीं होती

Lecture - 8 Chapter 6 Application of Derivatives

In this lecture, I am discussing more questions based on tangents and normals from NCERT Exercise 6.3

Questions discussed in this lecture:

NCERT EXERCISE 6.3 (Tangents and Normals)

Question 21. Find the equation of the normals to the curve \( y = x^3 + 2x + 6 \) which are parallel to the line x + 14y + 4 = 0.

Question 22. Find the equations of the tangent and normal to the parabola \( y^2 = 4ax \) at the point \(  (at^2, 2at)\).

Question 23. Prove that the curves \( x = y^2 \) and \( xy = k \) cut at right angles if \(  8k^2 = 1 \).

Question 24. Find the equations of the tangent and normal to the hyperbola \( \frac{x^2}{a^2} – \frac{y^2}{b^2} = 1 \) at the point \( (x_0, y_0) \).

Question 25. Find the equation of the tangent to the curve \( y = \sqrt{3x – 2} \), which is parallel to the line \( 4x – 2y + 5 = 0 \).

Choose the correct answer in Exercises 26 and 27.

Question 26. The slope of the normal to the curve \( y = 2x^2 + 3 sin x = 0 \) at x = 0 is
(A) 3
(B) 1/3
(C) -3
(D) -1/3

Question 27. The line y = x + 1 is a tangent to the curve \( y^2 = 4ax \) at the point
(A)  (1, 2)
(B)  (2, 1)
(C)  (1, -2)
(D)  (-1, 2)

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