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# 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)