FINDING LOCUS OF A POINT PRACTICE WORKSHEET

(1)  Find the locus of P, if for all values of α, the co-ordinates of a moving point P is

(i) (9cosα , 9 sinα)

(ii) (9 cosα , 6 sinα)            Solution

(2)  Find the locus of a point P that moves at a constant distant of (i) two units from the x-axis (ii) three units from the y-axis.               Solution

(3)  If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x = a cos³ θ, y = a sin³ θ.      Solution

(4)  Find the value of k and b, if the points P(−3, 1) and Q(2,b) lie on the locus of x² − 5x + ky = 0.   Solution

(5)  A straight rod of length 8 units slides with its ends A and B always on the x and y axes respectively. Find the locus of the mid point of the line segment AB    Solution

(6)  Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3, 5), (1,−1) is equal to 20   Solution

(7)  Find the equation of the locus of the point P such that the line segment AB, joining the points A(1,−6) and B(4,−2), subtends a right angle at P.    Solution

(8)  If O is origin and R is a variable point on y² = 4x, then find the equation of the locus of the mid-point of the line segment OR.    Solution

(9)  The coordinates of a moving point P are (a/2 (cosec θ + sin θ) , b/2 (cosecθ − sin θ)), where θ is a variable parameter. Show that the equation of the locus P is b²x² − a²y² = a²b² .    Solution

(10)  If P(2,−7) is a given point and Q is a point on 2x² + 9y² = 18, then find the equations of the locus of the mid-point of PQ.     Solution

(11)  If R is any point on the x-axis and Q is any point on the y-axis and P is a variable point on RQ with RP = b, PQ = a. then find the equation of locus of P.      Solution

(12)  If the points P(6, 2) and Q(−2, 1) and R are the vertices of a ΔPQR and R is the point on the locus y = x² − 3x + 4, then find the equation of the locus of centroid of ΔPQR                Solution

(13)  If Q is a point on the locus of x² + y² + 4x − 3y + 7 = 0, then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is origin. Solution

(14)  Find the points on the locus of points that are 3 units from x-axis and 5 units from the point (5, 1).   Solution

(15)  The sum of the distance of a moving point from the points (4, 0) and (−4, 0) is always 10 units. Find the equation of the locus of the moving point          Solution

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