Applications of Derivatives Lecture 8
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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 & 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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