अगर पाना है मंजिल तो, अपना रहनुमा खुद बनो,

वो अक्सर भटक जाते हैं, जिन्हें सहारा मिल जाता है।

# Lecture - 7 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 15.** Find the equation of the tangent line to the curve \( y = x^2 – 2x + 7 \) which is

(a) parallel to the line 2x – y + 9 = 0

(b) perpendicular to the line 5y – 15x = 13.

**Question 16.** Show that the tangents to the curve \( y = 7x^3 + 11\) at the points where x = 2 and x = – 2 are parallel.

**Question 17.** Find the points on the curve \( y = x^3\) at which the slope of the tangent is equal to the y-coordinate of the point.

**Question 18.** For the curve \( y = 4x^3 – 2x^5 \), find all the points at which the tangent passes through the origin.

**Question 19.** Find the points on the curve \( x^2 + y^2 -2x – 3 = 0 \) at which the tangents are parallel to the x-axis.

**Question 20.** Find the equation of the normal at the point \( (am^2, am^3) \) for the curve \( ay^2 = x^3 \).