*In this lecture, I am discussing basics of slope of tangent, slope of normal, slope of parallel lines, slope of perpendicular lines, equation of tangent, equation of normal and questions based on these topics from **NCERT Exercise 6.3*

**Questions discussed in this lecture:**

## NCERT EXERCISE 6.3 (Tangents & Normals)

**Question 1.** Find the slope of the tangent to the curve y = 3x^4 – 4x at x = 4.

**Question 2.** *Find the slope of the tangent to the curve y = \frac{x – 1}{x – 2}, x \ne 2 at x =10.*

**Question 3.** Find the slope of the tangent to curve y = x^3 – x + 1 at the point whose x-coordinate is 2.

**Question 4.** Find the slope of the tangent to curve y = x^3 – 3x + 2 at the point whose x-coordinate is 3.

**Question 5.** Find the slope of the normal to the curve x = a \cos^3 \theta, y = a \sin^3 \theta at \theta = \frac{\pi}{4}.

**Question 6.** *Find the slope of the normal to the curve x = 1 – a \sin \theta, y = b \cos^2 \theta at \theta = \frac{\pi}{2}.*

**Question 7.** Find points at which the tangent to the curve y = x^3 – 3x^2 – 9x + 7 is parallel to the x – axis.

**Question 8.** Find a point on the curve y = (x – 2)^2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

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मंजिल नहीं मिलती नाकाम इरादों से।