Question

7. Find the curve whose gradient at any point X-a P(x,y) on it is y-b through the origin. and which passes through the origin.​

Answer 1

Answer:

The gradient at any point P (x, y) on the curve is given by dy/dx According to the problem  dy/dx = (x - a)/(y - b) Separating the variables,  (y – b) dy = (x – a) dx  Integrating,  ∫(y – b) dy = ∫(x – a) dx (or) (y – b)2 = (x – a)2 + b2 – a2 is the required equation of the curve.Read more on Sarthaks.com - https://www.sarthaks.com/871565/find-the-curve-whose-gradient-at-any-point-x-y-on-it-is-x-a-and-which-passes-through-the-origin