रख हौसला वो मंजर भी आयेगा,

प्यासे के पास चल के समन्दर भी आयेगा,

थक कर न बैठ ऐ मंजिल के मुसाफिर,

मंजिल भी मिलेगी…

और मिलने का मज़ा भी आयेगा।

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 9.** Find the point on the curve \( y = x^3 – 11x + 5 \) at which the tangent is y = x – 11.

**Question 10.** Find the equation of all lines having slope – 1 that are tangents to the curve \( y = \frac{1}{x – 1}, x \ne 1 \).

**Question 11.** Find the equation of all lines having slope 2 that are tangents to the curve \( y = \frac{1}{x – 3}, x \ne 3 \).

**Question 12.** Find the equation of all lines having slope 0 that are tangents to the curve \( y = \frac{1}{x^2 – 2x + 3} \).

**Question 13.** Find points on the curve \( \frac{x^2}{9} + \frac{y^2}{16} = 1 \) at which the tangents are

(i) parallel to x-axis

(ii) parallel to y-axis

**Question 14.** Find the equations of the tangent and normal to the given curves at the indicated points:

(i) \( y = x^4 – 6x^3 + 13x^2 – 10x + 5 \text{ at } (0, 5) \)

(ii) \( y = x^4 – 6x^3 + 13x^2 – 10x + 5 \text{ at } (1, 3) \)

(iii) \( y = x^3 \text{ at } (1, 1) \)

(iv) \( y = x^2 \text{ at } (0, 0) \)

(v) \( x = \cos t, y = \sin t \text{ at } t = \frac{\pi}{4} \)