Misc 9 - Find area of smaller region x2/a2 + y2/b2 = 1 - Area between curve and line

Slide2.JPG
Slide3.JPG Slide4.JPG Slide5.JPG Slide6.JPG

  1. Class 12
  2. Important Question for exams Class 12
Ask Download

Transcript

Misc 9 Find the area of the smaller region bounded by the ellipse 2 2 + 2 2 =1 & + = 1 Step 1: Drawing figure + = is an which is a equation ellipse with as principle For + = 1 Points A(a, 0) and B(0, b) passes through both line and ellipse Required Area Required Area = Area OACB Area OAB Area OACB Area OACB = 0 Equation of ellipse 2 2 + 2 2 =1 2 2 =1 2 2 2 = 2 1 2 2 = 2 1 2 2 = 1 2 2 Therefore, Area OACB = 0 1 2 2 =b 0 2 2 2 = 0 2 2 = 1 2 2 2 + 2 2 sin 1 0 = 1 2 . 2 2 + 2 2 sin 1 1 2 0 2 0 2 + 2 2 sin 1 0 = 0+ 2 2 . 0 0 = 0+ 2 2 . = 2 2 2 = 4 Area OAB Area OAB = 0 Equation of line + =1 =1 = 1 Therefore, Area OAB = 0 1 = 2 2 0 = 2 2 0 0 2 2 = 2 0 = 2 Area Required = Area OACB Area OAB = 4 2 = 2 2 1 = 2 2 2 = square units

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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.