Graphing orthogonal trajectories
WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of eachfamilyonacommonscreen.1 y2 = kx3 First, we find the slopes of the given family. y2 = kx3 2ydy= 3kx2 dx 1 2ydx · dy= 1 2ydx ·3kx2 dx dy dx = 3kx2 2y From y2 = kx3 we get k= y2 x3. Substituting, dy dx = 3· y2 x3 · x2 2y dy dx = 3y 2x WebQuestion: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x^2 + 2y^2 = 5 k^2 Use a graphing device to draw several members of each family on a common screen. This problem has been solved! See the answer Show transcribed image text Expert Answer 100% (11 ratings)
Graphing orthogonal trajectories
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WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = 1+ kr y = (C – r)3 y = lC+r³ y = (C +x*)* y = VC- y = V3 + I+ C Question thumb_up 100% Transcribed Image Text: Find the orthogonal trajectories of the family of curves. WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. y = k/x Solution Verified 4.5 (9 …
WebFind the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. x^2+2y^2=k^2 x2 +2y2 = k2 Explanation Verified Reveal next step Reveal all steps Create a free account to see explanations Continue with Google Continue with Facebook Sign up with email Already … WebProcedure to find orthogonal trajectory: 1. Let f(x,y,c)=0 be the equation of the given family of curves, where c is an arbitrary parameter. 2. Differentiate f=0; w.r.t. 'x' and …
WebSince the orthogonal trajectories should have perpendicular tangent lines, their slopes will be negative reciprocals of the above. In other words, the orthogonal trajectories of … WebMar 3, 2024 · Finding Orthogonal Trajectories. Step 1. Find a differential equation \[y'=f(x,y) \nonumber \] for the given family. Step 2. Solve the differential equation \[y'=-{1\over f(x,y)} \nonumber \] to find the …
WebFind the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2 = 15k2 Use a graphing device to draw several members of each family on a … small kitchen appliance tableWebFind the orthogonal trajectories of the family of curves y= cx3 c x 3 Graph some examples of both families of curves. You can use Wolfram Alpha or any other graphing tool to create the... small kitchen appliance storesWebAug 28, 2024 · You have eliminated c in the fourth step to get the ODE for the orthogonal trajectories. Finally, in solving the last ODE you cannot use the same constan c. Use spmething else like k. So the x 2 + 2 y 2 = k … small kitchen appliance storageWebNow I have a differential equation, and the orthogonal trajectory should be represented by the negative reciprocal. d y d x = − 5 2 x y ∫ y d y = ∫ − 5 2 x d x y = − 5 4 x 2 + C This … small kitchen and dining roomWebMay 10, 2024 · Orthogonal Trajectories Consider two families of curves, circles and lines as shown in the figure. If you look at the intersection points, you’ll notice that these … high wycombe to bicester trainWebExample 2. Find the orthogonal trajectories to the family of curves y= cxn, where n is a fixed positive integer and can arbitrary constant. Solution. If n= 1, the curves are the family of rays from the origin, so the orthogonal trajectories should be the circles centered at the origin – this will help check our work. small kitchen appliance manufacturersWebtrajectory of the other family, then the two families are said to be orthogonal trajectories. A procedure for finding a family of orthogonal trajectories G(x,y,K) = 0 for a given family of curves F(x,y,C) = 0 is as follows: Step 1. Determine the differential equation for the given family F(x,y,C)=0. Step 2. Replace y0 in that equation by −1 ... high wycombe to birmingham airport