Check sibling questions

Ex 9.3, 7 - Family of Parabolas having vertex at origin, axis

Ex 9.3, 7 - Chapter 9 Class 12 Differential Equations - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Question 7 Form the differential equation of the family of Parabolas having vertex at origin and ๐‘Ž๐‘ฅ๐‘–๐‘  along positive ๐‘ฆโˆ’๐‘Ž๐‘ฅ๐‘–๐‘  Equation Of Parabola where vertex is at origin and axis along y-axis is ๐‘ฅ^2=4๐‘Ž๐‘ฆ Differentiating Both Sides w.r.t. ๐‘ฅ 2๐‘ฅ=4๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘ฅ=2๐‘Ž ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘ฅ=2๐‘Ž๐‘ฆ^โ€ฒ Dividing (2) by (1) i.e. (2) รท (1) ๐‘ฅ/๐‘ฅ^2 =(2๐‘Ž๐‘ฆ^โ€ฒ)/4๐‘Ž๐‘ฆ 1/๐‘ฅ=๐‘ฆ^โ€ฒ/2๐‘ฆ 2๐‘ฆ=๐‘ฅ๐‘ฆ^โ€ฒ โˆด ๐’™๐’š^โ€ฒโˆ’๐Ÿ๐’š=๐ŸŽ is the required differential equation

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.