# locus of a point formula

The given distance is the radius and the given point is the center of the circle.In 3-dimensions (space), we would define a sphere as the set of points in space a given distance from a given point. The sum of the squares of the distances from P to the points (a,0) and (-a,0) is 4b^2, where b >= a/sqrt of 2 > 0 b. the distance of P from the point (8,0) is twice its distance from the point (0,4). Example 6 Find the equation of set of points P such that PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7), respectively. A locus is a set of points that meet a given condition. 9,251 … The fixed point is the centre and the constant distant is the radius of the circle. Focal length. I need a general formula that calculates the equidistant locus of three points $(P_x,P_y)$; in terms of the coordinates of the three points $(A_x, A_y), (B_x,B_y), (C_x,C_y)$. Example: Let us construct a parabola as a locus: Create free Points A and B, and Line d lying through them (this will be the directrix of the parabola). share | cite | improve this question | follow | edited May 1 '14 at 5:44. Motion. (iii) Eliminate the parameters, so that the resulting equation contains only h, k and known quantities. If P is equidistant from A and B, then PA=BA Using the distance formula … This signifies to be present on the root locus, the point must necessarily satisfy the angle condition. Change this equation to polar form, we get : RcosΘ cosθ+ RsinΘ sinθ=r Rcos Θ−θ =r As this straight line passes through the point A(2, 0 o), we have ∴ 2cos 0°−θ =r ∴ r=2cosθ , which is already an equation for the locus of M in polar form ! You can then treat these expressions as parametric equations and u want to combine them so you may eliminate your parameter, which in this case is t. Done in a way that not only it is relatable and easy … Could one help me ? Equation of Locus: The equation of locus is an equation which is satisfied by all the points satisfying given the geometrical condition in the problem Steps Involved in Finding Equation of Locus: Assume the locus point P(x, y) Write given geometrical condition; Use distance, section, centroid, and other formulae as per condition The locus of points equidistant from two given points is the perpendicular bisector of the segment that joins the two points. In this tutorial I look at the locus of a point which moves along the arc of a circle. r=2cosθ is an equation of a circle. LocusEquation(

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