Minimum distance between the parabolas y² – 4x –8y + 40 = 0 and x² –8x –4y + 40 = 0 is (A) 0 (B) 3 (C) 2 2 (D) E
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A: Steps are shown just try to have (a±b)2 , by substituting any number by substraction and addition.
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A: perpendicular distance
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A: The solution is given below. .
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Q: Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =k
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Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D
A: Topic = Geometry
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- What do you mean by asymptotically stable for autonomous equations ?find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1) (-1,1) (1,1) (1,-1)Find the point on the planez = x + y + 1closest to the point P = (1, 0, 0). Hint: Minimize the square of thedistance.
- By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1 and u = y2, find the minimum distance in the xy-plane from the line y = x + 1 to the pa-rabola y2 = x.Find the family of orthogonal trajectories of the family of hyperbolas x²-4y² =kfind the maximum value that f(x, y, z) = x^2 + 2y - z^2 can have on the line of intersection of the planes 2x-y = 0 and y + z = 0 Can this problem be solved using lagrange multipliers?
- Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0) and show that ƒ takes on a minimum there.The orthogonal trajectories to the family of hyperbolas xy= C is given by the family 1)y=cx 2)y2 -x2 =c 3)y2+x2 =c 4)x=cx2Solve for y2 by using reduction of order And for nonhomogeneous using undetermined coefficients linear mathematics
- Let y be the solution of the initial value problemy" +y = - sin(2x), y (0) = 0, y'(0) = 0.The maximum value of y isFind all points (x, y) where f(x, y) has a possible relative maximum or minimum.Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the planes 2x - y = 0 and y + z = 0.