Misc 23 - Normal to x2 = 4y passing (1,2) is (a) x + y = 3 - Finding equation of tangent/normal when point and curve is given

Slide46.JPG
Slide47.JPG Slide48.JPG

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
Ask Download

Transcript

Misc. 23 The normal to the curve ๏ท๐‘ฅ๏ทฎ2๏ทฏ=4๐‘ฆ passing (1,2) is (๐ด) ๐‘ฅ + ๐‘ฆ = 3 (๐ต) ๐‘ฅ โ€“ ๐‘ฆ = 3 (๐ถ) ๐‘ฅ + ๐‘ฆ = 1 (๐ท) ๐‘ฅ โ€“ ๐‘ฆ = 1 Since (1, 2) lies on normal, it will satisfy its equation Option 1 Equation of Normal is ๐‘ฅ+๐‘ฆ=3 Putting ๐‘ฅ=1 & ๐‘ฆ=2 in equation ๐‘ฅ+๐‘ฆ=3 1+2=3 3=3 Thus, ๏ท1 , 2๏ทฏ Satisfy the Equation of Normal Hence ๐‘ฅ+๐‘ฆ=3 is Required Equation of Normal Option 2 If equation of Normal is ๐‘ฅโˆ’๐‘ฆ=3 Putting ๐‘ฅ=1 & ๐‘ฆ=2 in equation ๐‘ฅโˆ’๐‘ฆ=3 1โˆ’2=3 โˆ’1=3 But โˆ’1โ‰ 3 Hence ๐‘ฅโˆ’๐‘ฆ=3 is not the equation of Normal Option 3 If Equation of Normal is ๐‘ฅ+๐‘ฆ=1 Putting ๐‘ฅ=1 & ๐‘ฆ=2 in equation โ‡’ ๐‘ฅ+๐‘ฆ=1 โ‡’ 1+2=1 โ‡’ 3=1 But, 3โ‰ 1 Hence ๐‘ฅ+๐‘ฆ=1 is not Required Equation of Normal Option 4 If Equation of Normal is ๐‘ฅโˆ’๐‘ฆ=1 Putting ๐‘ฅ=1 & ๐‘ฆ=2 in equation โ‡’ ๐‘ฅโˆ’๐‘ฆ=1 โ‡’ 1โˆ’2=1 โ‡’ โˆ’1=1 Since โˆ’1โ‰ 1 Hence ๐‘ฅโˆ’๐‘ฆ=1 is not Required Equation of Normal Hence Correct Answer is (A)

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail