LOCUS
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1) Find the locus of the point which moves such that its distance from the points (3,1) and (-2,5) are always equal. 10x - 8y + 19= 0
2) Find the locus of a point of which moves so that it is always at a distance 4 from (1,-2). x²+y²- 2x + 4y - 11= 0
3) Find the locus of a point which moves so that its distance from your (4,0) is always twice its distance from (1,0). x²+y²= 4
4) A and B are two fixed points whose coordinates are (2,1) and (3,2) respectively. A point P moves in such a way that OA= 2PB always. find the locus of P. 3x² + 3y² - 20x - 14y+47= 0
5) Find the locus of a moving point so that its distance from (0, 4) is two-thirds of its distance from (0,9). x²+ y²=36
6) The co-ordinates of two points A and B are (-5,3) and (2,4) respectively. Find the locus of P(x,y) such that PA: PB= 3:2 5x²+5y²-76x-48y+ 44=0.
7) A point moves so that its distance from the point (a,0) exceeds the distances from axis of y by a. find the locus. y²= 4ax
8) find the locus of a point which moves so that its distance from the y-axis is double its distance from the distance from the point (2,2). 3x²+ 4y²-16x-16y+32= 0
9) find the locus of a point which moves such that its distance from the point (4,0) is √2 times of its its of its its times of its its of its distance from the y axis. x²- y² + 8x - 16= 0.
10) Find the locus of a point which moves so that its distance from the point (0,5) is two-thirds of its distance from x axis. 9x²+ 5y²- 90y + 225= 0
11) The point A and B are (-4,0) and (-1,0) respectively. A point P moves in such a way that PA:PB = 2:. find the locus of P. x²+y²=4
12) Find the locus of a point which moves so that the sum of the squares of its distances from the two points (3,0) (-3,0) is 36. x²+ y²= 9.
13) Find the locus of a point which moves so that the sum of the squares so that the sum of the squares of its distances from the point (3,0) and (-3,0) is always equal to 50. x²+ y²=16
14) Find the locus of a point which moves so that sum of its distances from the points (4,0) and (-4,0) is 10. 9x²+ 25y²= 225
15) Find the locus of a point which moves such that the difference of its distances from (2,5) and (6,5) is 2. 3x²-y²-24x+10y +20= 0
16) Find the locus of the centre of the circles passing through the the point (c,0) and (-c,0). x= 0
17) A(2,-3) and B(4,0) are two points. Find the locus of a point P such that the area of the triangle PAB is always 4 units. 3x-2y=4
18) A line segment, 16 units in length, moves so that its ends are always on the positive co-ordinate Axis. Find the equation of the locus of its midpoint. x²+y²= 64
19) If the coordinates of two vertices of a triangle be A(-3,0) and B(3,0) and angle ACB is 90, find the locus of centroid of the triangle. x²+ y² = 1
20) The co-ordinates of a moving point P are ((a sec t, b tan t), where t is a variable parameter. Find the locus of the point P. x²/a² - y²/b² = 11.
21) The co-ordinates of a moving point P are {{(t-1)/(t+1), (2t+1)/(t+1)}, where t is a variable parameter. Find the locus of the point P. x - 2y+3= 0
22) AB is a line of fixed length, 66 units, joining the points A((t,0) and B which lies on positive y-axis. P is a point on AB distant 2 units from A. Express the coordinates of B and of P in terms of t. Find the locus of P as a t varies. x²+ 4y²= 16
23) Show that the locus of the point of intersection of straight lines. x sin t - y(cos t -1)= a sin t; x sin t - y(cos t -1)= - a siin t is x²+ y²= a².
24) Show that (1,2) lies on the locus x²+y²-4x- 6y +11= 0
25) Does the point (3,0) lie on the curve 3x²+y²- 4x +7= 0. No
26) Find the condition that the point (h,k) may lie on the curve x²+y²+5x+11y-2= 0. h² + k²+ 5h + 11k- 2= 0.
27) If the line (2+k)x - (2- k)y +(4k+14)= 0 passes through the point (-1,21), find k. 5/4
28) Find the ratio in which the line joining the points (6,12) and (4,9) is divided by the curve. x²+ y²= 4.
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