Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg
Example 17 - Chapter 6 Class 12 Application of Derivatives
Last updated at Jan. 7, 2020 by Teachoo
Transcript
Example 17 Find points on the curve ๐ฅ^2/4 + ๐ฆ^2/25 = 1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. Given curve ๐ฅ^2/4 + ๐ฆ^2/25 = 1 Slope of the tangent is ๐๐ฆ/๐๐ฅ Finding ๐ ๐/๐ ๐ 2๐ฅ/4+(2๐ฆ ๐๐ฆ/๐๐ฅ)/25 = 0 ๐ฅ/2 + 2๐ฆ/25 ๐๐ฆ/๐๐ฅ = 0 2๐ฆ/25 ๐๐ฆ/๐๐ฅ = (โ๐ฅ)/2 ๐๐ฆ/๐๐ฅ = (โ๐ฅ)/2 ร 25/2๐ฆ ๐๐ฆ/๐๐ฅ = (โ25๐ฅ)/4๐ฆ Hence, ๐๐ฆ/๐๐ฅ = โ (โ25๐ฅ)/4๐ฆ (i) Tangent is parallel to x-axis If the tangent is parallel to x โ axis, its slope is 0 Hence, ๐๐ฆ/๐๐ฅ = 0 (โ25๐ฅ)/4๐ฆ = 0 x = 0 Putting x = 0 in equation of the curve ๐ฅ^2/4 + ๐ฆ^2/25 = 1 0/4 + ๐ฆ^2/25 = 1 ๐ฆ^2 = 25 y = ยฑ 5 Hence, the points are (0, 5) and (0, โ5) (ii) Tangent is parallel to y-axis If the tangent is parallel to y โ axis, its slope is 1/0 Hence, ๐๐ฆ/๐๐ฅ = 1/0 (โ25๐ฅ)/4๐ฆ = 1/0 y = 0 Putting y = 0 in equation of the curve ๐ฅ^2/4 + ๐ฆ^2/25 = 1 ๐ฅ^2/4 + 0/25 = 1 ๐ฅ^2/4 = 1 x2 = 4 x = ยฑ 2 Hence, the points are (2, 0) and (โ2, 0)
Examples
Example 1
Example 2
Example 3
Example 4 Important
Example 5
Example 6
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 You are here
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
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
Example 43 Important
Example 44 Important
Example 45 Important
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50 Important
Example 51
Chapter 6 Class 12 Application of Derivatives
Serial order wise
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.