**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

After having gone through the stuff given above, we hope that the students would have understood "Finding Locus of a Point Practice Worksheet".

Apart from the stuff given above, if you want to know more about "Finding Locus of a Point Practice Worksheet". Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**