WebThis circle will have the same x, y coordinates and that is equal to the radius of the circle. The equation becomes, x-α 2 + y-α 2 = α 2. where a is a parameter. Since there is only one parameter, the equation is of order 1. Therefore, the differential equation is of order 1. Hence, the correct answer is Option (A).

Differential Equations: Families of Circles with center on the line y ...

WebSolution. Verified by Toppr. Correct option is B) Any circle with given radius can be written as, (x−h) 2+(y−k) 2=a 2. Where (h,k) be the center of the circle which is variable. So in above algebraic equation , there are two arbitrary constants h and k. Hence order of differential equation corresponding to above equation will be 2nd order. WebApr 12, 2024 · The differentiation should be done twice as radius if given and there are only two variables h, k that we are dealing with. Complete step-by-step answer: As we know … japanese manly wharf

Answered: Obtain the differential equation of all… bartleby

WebMar 27, 2024 · So, The equation of circle = (x − a) 2 + (y − a) 2 = a 2 ----- (1) On differentiating with respect to x, we get 2 (x - a) + 2 (y - a) d y d x = 0 ⇒ x + y d y d x = a (1 + d y d x) ⇒ a = … WebMar 30, 2024 · 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 … WebMar 3, 2024 · x2 + y2 + c2 = 0. does not define a one-parameter family of curves, since no (x, y) satisfies the equation if c ≠ 0, and only the single point (0, 0) satisfies it if c = 0. Recall … lowe\u0027s illinois rd