## Find the equation of the normal to the curve y = ๐ฅ + 1/x, x > 0 perpendicular to the line 3๐ฅ − 4๐ฆ = 7.

Last updated at Oct. 21, 2020 by Teachoo

Transcript

Question 22 Find the equation of the normal to the curve y = ๐ฅ + 1/๐ฅ, x > 0 perpendicular to the line 3๐ฅ โ 4๐ฆ = 7 Finding Slope y = x + 1/๐ฅ Differentiating both sides ๐๐ฆ/๐๐ฅ = 1 โ 1/๐ฅ^2 Now, Slope of Normal = (โ๐)/(๐ โ ๐/๐^๐ ) Given that Normal is perpendicular to 3x โ 4y = 7 So, Slope of Normal ร Slope of Line = โ1 (โ1)/(1 โ 1/๐ฅ^2 ) ร 3/4 = โ1 3/4 = 1 โ 1/๐ฅ^2 1 โ 1/๐ฅ^2 = 3/4 1 โ 3/4 = 1/๐ฅ^2 1/4 = 1/๐ฅ^2 x2 = 4 x = ยฑ 2 Since x > 0 โด x = 2 Finding y when x = 2 y = x + 1/๐ฅ y = 2 + 1/2 y = ๐/๐ Now, Slope of Normal is (โ๐)/๐ and it passes through point (2, ๐/๐) So, equation of Normal is (y โ y1) = m (x โ x1) y โ 5/2 = โ 4/3 (x โ 2) y โ 5/2 = โ 4/3x + 8/3 Multiplying both sides by 6 6y โ 6 ร 5/2 = โ6 ร 4/3x + 6 ร 8/3 6y โ 15 = โ8x + 16 8x + 6y = 31

CBSE Class 12 Sample Paper for 2021 Boards

Question 1 (Choice 1)

Question 1 (Choice 2)

Question 2

Question 3 (Choice 1)

Question 3 (Choice 2)

Question 4

Question 5 โ Choice 1

Question 5 (Choice 2)

Question 6

Question 7 (Choice 1)

Question 7 (Choice 2)

Question 8

Question 9 (Choice 1)

Question 9 (Choice 2)

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20 (Choice 1)

Question 20 (Choice 2)

Question 21

Question 22 You are here

Question 23 (Choice 1)

Question 23 (Choice 2)

Question 24

Question 25

Question 26

Question 27

Question 28 (Choice 1)

Question 28 (Choice 2)

Question 29

Question 30

Question 31 (Choice 1)

Question 31 (Choice 2)

Question 32

Question 33

Question 34 (Choice 1)

Question 34 (Choice 2)

Question 35

Question 36 (Choice 1)

Question 36 (Choice 2)

Question 37 (Choice 1)

Question 37 (Choice 2)

Question 38 (Choice 1)

Question 38 (Choice 2)

Class 12

Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.