Last updated at April 19, 2021 by

Transcript

Example 19 Find the equations of the tangent and normal to the curve π₯^(2/3) + π¦^(2/3) = 2 at (1, 1).Given curve π₯^(2/3) + π¦^(2/3) = 2 Differentiating both sides w.r.t x 2/3 π₯^(1 β 2/3)+2/3 π¦^(1 β 2/3) ππ¦/ππ₯ = 0 2/3 π₯^((β1)/3)+2/3 π¦^((β1)/3) ππ¦/ππ₯ = 0 2/3 π¦^((β1)/3) ππ¦/ππ₯ = (β2)/3 π₯^((β1)/3) 1/π¦^(1/3) ππ¦/ππ₯ = (β1)/π₯^(1/3) π π/π π = β (π/π)^(π/π) Thus, Slope of tangent to the curve = β (π¦/π₯)^(1/3) At point (1, 1) Slope = β (π/π)^(π/π) = β1 Hence, Equation of tangent at point (1, 1) and with slope β1 is π¦β1=β1 (π₯β1) π¦β1=βπ₯+1 π+πβπ = π Also, Slope of Normal = (β1)/(πππππ ππ π‘ππππππ‘) = (β1)/(β1) = 1 Thus, Equation of normal at point (1, 1) and with slope 1 is π¦ β 1 = 1 (π₯ β 1) π¦ β 1 = π₯ β 1 π¦ =π₯ π βπ=π

Examples

Example 1
Deleted for CBSE Board 2022 Exams

Example 2 Deleted for CBSE Board 2022 Exams

Example 3 Deleted for CBSE Board 2022 Exams

Example 4 Important Deleted for CBSE Board 2022 Exams

Example 5 Deleted for CBSE Board 2022 Exams

Example 6 Deleted for CBSE Board 2022 Exams

Example 7

Example 8 Important

Example 9 Important

Example 10

Example 11 Important

Example 12

Example 13 Important

Example 14

Example 15

Example 16

Example 17 Important

Example 18

Example 19 You are here

Example 20

Example 21 Deleted for CBSE Board 2022 Exams

Example 22 Deleted for CBSE Board 2022 Exams

Example 23 Deleted for CBSE Board 2022 Exams

Example 24 Deleted for CBSE Board 2022 Exams

Example 25 Deleted for CBSE Board 2022 Exams

Example 26

Example 27

Example 28 Important

Example 29

Example 30 Important

Example 31

Example 32 Important

Example 33 Important

Example 34

Example 35 Important

Example 36

Example 37 Important

Example 38 Important

Example 39

Example 40 Important

Example 41 Important

Example 42 Important Deleted for CBSE Board 2022 Exams

Example 43 Important Deleted for CBSE Board 2022 Exams

Example 44 Important Deleted for CBSE Board 2022 Exams

Example 45 Important Deleted for CBSE Board 2022 Exams

Example 46 Important

Example 47 Important

Example 48 Important

Example 49 Deleted for CBSE Board 2022 Exams

Example 50 Important

Example 51

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.