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