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Find out the differential equation of the following two families of curves : Straight lines having slope and $x$-intercept equal in magnitude. Straight lines at a fixed distance $p$ from the origin.
- Find the differential equation for a family of curves
Thus, to figure out the answer, pick an arbitrary point...
- Find the differential equation for a family of curves
Thus, to figure out the answer, pick an arbitrary point $(x_0, y_0)$ in the plane; find the equations of the circles in your family that intersect $(x_0, y_0)$; find $\frac{dy}{dx}$ at $(x_0, y_0)$ for each of those circles, giving two values $r_0(x_0, y_0)$ and $r_1(x_0, y_0)$ (or 1 value $r_0 = r_1$ if you have a degeneracy); and construct ...
Represent each of the following as an n-parameter family of curves | i.e., represent it by an equation in x and y with n additional variables, where n is as low as possible.
4 dni temu · A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for example, in the solutions to differential equations with a free parameter (Harris and Stocker 1998, p. 649).
Live Math Tutorial Families of Curves
10 lis 2020 · What if we would like to start with the equation of a curve and determine a pair of parametric equations for that curve? This is certainly possible, and in fact it is possible to do so in many different ways for a given curve. The process is known as parameterization of a curve.
In geometry, a family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter (s) influence the shape of the curve in a way that is more complicated than a simple linear transformation.
