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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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