x = 0, x=0, x = 0, which gives a line perpendicular to the original line through the point; this makes sense geometrically as well. Firstly, writing the characteristic equation of the above system, So, from the above equation, we get, s = 0, -5 and -10. This can be written as. Now to the equation. Solution: Let P(x. y) be the point on the locus and … □_\square□. Further informations and examples on geogebra.org. Find an equation for the set of all points (x,y) satisfying the given condition: The product of its distances from the coordinate axes is 4. answer: xy= plus or minus 4 Please show how you have come up with your answer. The next part will cover the remaining examples. a=0,a=0,a=0, the equation reduces to x2=0, x^2=0,x2=0, or x=0,x=0,x=0, which gives a line perpendicular to the original line through the point; this makes sense geometrically as well. x 2 = 0, x^2=0, x2 = 0, or. Show that the equation of the locus P is b 2 x 2 − a 2 y 2 = a 2 b 2. There is also another possibility of y = -5, also a line parallel to the X-axis, at a distance of 5 units, but lying below the axis. d_1+d_2 &= c \\ Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. botasnegras shared this question 10 years ago . p² + q² + 4p - 6q = 12. Find the equation of the locus of P, if A = (2, 3), B = (2, –3) and PA + PB = 8. class-11; Share It On Facebook Twitter Email. It is given that OP = 4 (where O is the origin). The answer is reported as 8x^2 - y^2 -2x +2y -2 = 0, which i failed to get. Sign up to read all wikis and quizzes in math, science, and engineering topics. Log in here. Well, that’s it! 6.6 Equation of a Locus. Equation to a locus, and equation of a curve in general, in coordinate geometry Definition of a Locus Locus is a Latin word which means "place". I’ll again split it into two parts due to its length. Hence the equation of locus y 2 = 2x. I need your help. (Hi) there, I was unable to solve the following questions, please help me. Already have an account? Answered. Equation of locus. Example – 37: Find the equation of locus of a point such that the sum of its distances from co-ordinate axes is thrice its distance from the origin. Let PA=d1PA = d_1PA=d1 and PB=d2. At times the curve may be defined by a set of conditions rather than by an equation, though an … Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The equation of a curve is the relation that holds true between the coordinates of all the points on the curve, and no other point except that on the curve. Many geometric shapes are most naturally and easily described as loci. We have to construct the root locus for this system and predict the stability of the same. Therefore, the equation to the locus under the given conditions is x2 + y2 = 16. Forgot password? \(\sqrt{(x-1)^2+(y-1)^2}=\sqrt{(x-2)^2+(y-4)^2}\). Find the locus of a point P that has a given ratio of distances k = d1/d2 to two given points. or, x + 3y = 4 ……… (1) Which is the required equation to the locus of the moving point. Q) Find the equation of the locus of a point P whose distance from (-1,1) is equal to thrice it's distance from the Y-axis. Suppose the constant is c2, c^2,c2, c≠0. Find the locus of all points P PP in a plane such that the sum of the distances PAPAPA and PBPBPB is a fixed constant, where AAA and BBB are two fixed points in the plane. To find the equation to a locus, we start by converting the given conditions to mathematical equations. 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