Locus of a point-Determining the equation of a curve

A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve.

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Please see the attached file for complete solution along with a diagram.

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A curve is traced by a point P(x,y) which ...

Solution Summary

Solution involves finding the locus of a point in the x-y plane. Solution is presented in an easy to understand manner along with a diagram.

Please help me with the attached root locus design question (see attachment).
(Involves: plotting the root locus, determining gain, designing a proportional and integral controller, determining the location of the controller zero, and finding the required controller gain).

In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6).
a) The family dog is walking through the backyard so that it is at all times twice as far From A as it is from B. Find theequation of thelocus of the dog. Draw a graph that shows the two trees, the path of the dog. and the ralationship defining

Draw the positive and negative gain root-locus of (view attachment to see L equation). Hence find the gain to have a closed loop damping factor (0.7).
Please view attachment to see full question as it was not possible to type it all out.

How do you find theequation of thecurve of intersection of the surfaces
z = x^2 and x^2 + y^2 =1?
How can I show that thecurve with parametric equations
x = sin t, y = cos t, z = sin^2 t
is thecurve of intersection of these two surfaces?

Task: Apply curve-fitting techniques and interpret the results. As such, your work will include doing scatterplots, determining theequation and graph of thecurve on the scatterplot, finding the r^2 value, estimation using thecurve, etc. Using a linear model, you are expected to use the data given below (University of Maryland

Given thecurve
y = ax3 + bx2 + cx + d, a ≠ 0
Find the relation between the parameters a, b, and c that will ensure that thecurve:
(a) has only one turning point.
(b) has no turning points.
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Find an equation of the tangent to thecurve:
x = tan (theta), y = sec (theta)
at the point (1, sqrt(2)) by two methods: (a) without eliminating the parameter, and (b) by first eliminating the parameter.