

Ex 9.3
Ex 9.3, 2 Deleted for CBSE Board 2022 Exams
Ex 9.3, 3 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 4 Deleted for CBSE Board 2022 Exams
Ex 9.3, 5 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 6 Deleted for CBSE Board 2022 Exams You are here
Ex 9.3, 7 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 8 Deleted for CBSE Board 2022 Exams
Ex 9.3, 9 Deleted for CBSE Board 2022 Exams
Ex 9.3, 10 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2022 Exams
Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2022 Exams
Last updated at Dec. 10, 2019 by Teachoo
Ex 9.3, 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.