Finding Locus of a Point Practice Worksheet
Here we are going to see how to find equation of locus of a point with the given condition.
(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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