**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 cos^{3} θ, y = a sin^{3} 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 x^{2} − 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 y^{2} = 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 b^{2}x^{2} − a^{2}y^{2} = a^{2}b^{2} . Solution

(10) If P(2,−7) is a given point and Q is a point on 2x^{2} + 9y^{2} = 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 = x^{2} − 3x + 4, then find the equation of the locus of centroid of ΔPQR Solution

(13) If Q is a point on the locus of x^{2} + y^{2} + 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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