Question 6 - Forming Differential equations - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Forming Differential equations
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams You are here
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 8 Deleted for CBSE Board 2024 Exams
Question 9 Deleted for CBSE Board 2024 Exams
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 (MCQ) Deleted for CBSE Board 2024 Exams
Question 12 (MCQ) Important Deleted for CBSE Board 2024 Exams
Forming Differential equations
Last updated at April 16, 2024 by Teachoo
Question 6 Form the differential equation of the family of circle touching the 𝑦−𝑎𝑥𝑖𝑠 at origin. General Equation of Circle (𝑥−𝑎)^2+(𝑦−𝑏)^2=𝑟^2 where Centre at (𝑎 , 𝑏) and Radius is r If circle touches y-axis at origin, Center will be at x-axis So, Center = (a, 0) & Radius = a Thus, equation of circle becomes (𝑥−𝑎)^2+(𝑦−0)^2=𝑎^2 (𝑥−𝑎)^2+𝑦^2=𝑎^2 𝑥^2+𝑎^2−2𝑎𝑥+𝑦^2=𝑎^2 𝑥^2−2𝑎𝑥+𝑦^2=𝑎^2−𝑎^2 𝑥^2−2𝑎𝑥+𝑦^2=0 2𝑎𝑥=𝑥^2+𝑦^2 Differentiating Both Sides w.r.t. 𝑥 (𝑑(2𝑎𝑥))/𝑑𝑥=𝑑(𝑥^2 )/𝑑𝑥+𝑑(𝑦^2 )/𝑑𝑥 2a = 2x + 2y 𝑑𝑦/𝑑𝑥 a = x + yy’ …(1) …(2) From (1) 2𝑎𝑥=𝑥^2+𝑦^2 Putting value of a from (2) 2𝑥(𝑥+𝑦𝑦^′)=𝑥^2+𝑦^2 2𝑥^2+2𝑥𝑦𝑦^′=𝑥^2+𝑦^2 2𝑥^2−𝑥^2+2𝑥𝑦𝑦^′=+𝑦^2 𝟐𝒙𝒚𝒚^′+𝒙^𝟐=𝒚^𝟐 is the required differential equation.